Home |
Search |
Today's Posts |
#1
|
|||
|
|||
Experimental Evidence for Dynamic Doppler Shift
THE HYPOTHESIS:
Assuming that the equation for the Doppler frequency shift of a source moving at constant velocity also applies under dynamically changing velocity conditions, one would expect the propagating sound, that is produced by a high-frequency source moving dynamically at a low frequency around a fixed position, to be frequency modulated. One would further expect that the instantaneous frequency of the propagating sound would reflect the dynamic low-frequency velocity the source. If so, the waveform of the fm-demodulated high-frequency propagating sound, should follow on an instantaneous basis, the dynamic velocity of the low-frequency velocity of the source. THE SETUP: A small circular piezoelectric bimorph, having a resonant frequency of approximately 10KHz was attached to the 10-lb armature/shaft of a linear motor. The displacement of the armature/shaft was monitored by a linear displacement transducer attached to the opposite end of the armature/shaft. The linear displacement transducer also provided feedback for the servo amplifier which was driving the linear motor. Because the linear motor was in a servo loop, the displacement of the motor followed with reasonable accuracy both sinusoidal and non-sinusoidal command signals that were applied to the amplifier. The piezoelectric sound source was driven by a low-distortion oscillator at 10KHz. The sound emitted by the source was measured by a microphone at a distance of approximately one foot. The output of the microphone was amplified, high-pass filtered and applied to a frequency-to-voltage converter. The output of the frequency-to-voltage converter was low-pass filtered to reduce the level of the residual 10KHz carrier, amplified and applied to a signal averager. The signal averager was triggered by the command signal that was applied to the linear motor. Averaging was used in order to remove non-coherent 60Hz that was present in the output of the demodulator. THE MOTION OF THE SOUND SOURCE A triangular command signal having a 50-msec period was applied to the servo amplifier. A triangular command signal was used in order to simplify interpretation of the measurement result and to avoid the phase shift vs time delay ambiguity that would otherwise exist with fixed frequency sinusoidal excitation. The output of the displacement transducer was monitored on an oscilloscope and found to be triangular with rounded corners. The rounding of the corners is due to the limited closed-bandwidth of the servo. The velocity of the linear motor was therefore trapezoidal with relatively flat and relatively long plateaus and relatively short transitions. THE MEASUREMENT RESULT The propagating 10KHz signal emitted by the piezo bimorph was applied to an FFT analyzer in zoom-analysis mode with a resolution bandwidth of 0.1Hz. When the piezo bimorph was stationary, the propagating signal picked up by the microphone showed only a single spectral peak at 10KHz. When the piezo transducer was moving back and forth with a triangular displacement provided by the linear motor, the propagating signal received by the microphone contained numerous sidebands which were indicative of FM modulation. Additionally, the output of the FM demodulator was observed to be trapezoidal and followed on an instantaneous basis the velocity of the linear motor and the attached piezo transducer. THE CHALLENGE In science, theory usually follows experimental results. In this case the experimental result shows that a 10KHz signal applied to a small piezoelectric source moving back and forth around a fixed position becomes frequency modulated by the back and forth motion of the source. The measurement further shows that the received, FM-demodulated signal follows the instantaneous velocity of the source. This result is exactly what is expected on the basis of Doppler frequency shift extrapolated from constant velocity to dynamic velocity conditions. While some might argue that the observed FM-like sidebands and the trapezoidal demodulated waveform are the result of IM distortion, and not Doppler FM, the ball is in their court. It is now up to them to provide an explanation/analysis involving an IM producing mechanism in the present experimental setup that accounts for the present experimental result. Finally, it must be noted that the purpose of the present measurement was to demonstrate fundamental phenomenological behavior. The 10KHz carrier and the 50-msec peridiocity for the displacement of the linear motor were chosen solely to accommodate the hardware on hand. There is presently no reason to believe that the outcome of the present measurement would be different if other carrier frequencies or other source displacement periodicities or waveshapes were used. |
#2
|
|||
|
|||
"The Ghost" wrote in message om... THE HYPOTHESIS: Assuming that the equation for the Doppler frequency shift of a source moving at constant velocity also applies under dynamically changing velocity conditions, one would expect the propagating sound, that is produced by a high-frequency source moving dynamically at a low frequency around a fixed position, to be frequency modulated. One would further expect that the instantaneous frequency of the propagating sound would reflect the dynamic low-frequency velocity the source. If so, the waveform of the fm-demodulated high-frequency propagating sound, should follow on an instantaneous basis, the dynamic velocity of the low-frequency velocity of the source. THE SETUP: A small circular piezoelectric bimorph, having a resonant frequency of approximately 10KHz was attached to the 10-lb armature/shaft of a linear motor. The displacement of the armature/shaft was monitored by a linear displacement transducer attached to the opposite end of the armature/shaft. The linear displacement transducer also provided feedback for the servo amplifier which was driving the linear motor. Because the linear motor was in a servo loop, the displacement of the motor followed with reasonable accuracy both sinusoidal and non-sinusoidal command signals that were applied to the amplifier. The piezoelectric sound source was driven by a low-distortion oscillator at 10KHz. The sound emitted by the source was measured by a microphone at a distance of approximately one foot. The output of the microphone was amplified, high-pass filtered and applied to a frequency-to-voltage converter. The output of the frequency-to-voltage converter was low-pass filtered to reduce the level of the residual 10KHz carrier, amplified and applied to a signal averager. The signal averager was triggered by the command signal that was applied to the linear motor. Averaging was used in order to remove non-coherent 60Hz that was present in the output of the demodulator. THE MOTION OF THE SOUND SOURCE A triangular command signal having a 50-msec period was applied to the servo amplifier. A triangular command signal was used in order to simplify interpretation of the measurement result and to avoid the phase shift vs time delay ambiguity that would otherwise exist with fixed frequency sinusoidal excitation. The output of the displacement transducer was monitored on an oscilloscope and found to be triangular with rounded corners. The rounding of the corners is due to the limited closed-bandwidth of the servo. The velocity of the linear motor was therefore trapezoidal with relatively flat and relatively long plateaus and relatively short transitions. THE MEASUREMENT RESULT The propagating 10KHz signal emitted by the piezo bimorph was applied to an FFT analyzer in zoom-analysis mode with a resolution bandwidth of 0.1Hz. When the piezo bimorph was stationary, the propagating signal picked up by the microphone showed only a single spectral peak at 10KHz. When the piezo transducer was moving back and forth with a triangular displacement provided by the linear motor, the propagating signal received by the microphone contained numerous sidebands which were indicative of FM modulation. Additionally, the output of the FM demodulator was observed to be trapezoidal and followed on an instantaneous basis the velocity of the linear motor and the attached piezo transducer. THE CHALLENGE In science, theory usually follows experimental results. In this case the experimental result shows that a 10KHz signal applied to a small piezoelectric source moving back and forth around a fixed position becomes frequency modulated by the back and forth motion of the source. The measurement further shows that the received, FM-demodulated signal follows the instantaneous velocity of the source. This result is exactly what is expected on the basis of Doppler frequency shift extrapolated from constant velocity to dynamic velocity conditions. While some might argue that the observed FM-like sidebands and the trapezoidal demodulated waveform are the result of IM distortion, and not Doppler FM, the ball is in their court. It is now up to them to provide an explanation/analysis involving an IM producing mechanism in the present experimental setup that accounts for the present experimental result. Finally, it must be noted that the purpose of the present measurement was to demonstrate fundamental phenomenological behavior. The 10KHz carrier and the 50-msec peridiocity for the displacement of the linear motor were chosen solely to accommodate the hardware on hand. There is presently no reason to believe that the outcome of the present measurement would be different if other carrier frequencies or other source displacement periodicities or waveshapes were used. This experiment is very "pure", and in fact, pretty much *defines* the Doppler effect and frequency modulation. To determine its relevance to audio applications, someone now needs to add additional parameters. For example: o It would be interesting to observe the results when the modulating frequency and the carrier are close together in frequency, and the sidebands significantly overlap the modulating frequency, as they would in a typical loudspeaker. o Is the Doppler effect of the same order of magnitude of other loudspeaker nonlinearities, such as harmonic and intermodulation distortion? How difficult is it to resolve these effects separately when occurring simultaneously in the same loudspeaker? o How much do multi-way speakers mitigate these effects? Are wide-range drivers measurably worse in these effects? (My intuition predicts that they will be, but some full range speakers manage to employ mechanical crossovers -- but I would expect them to be ineffective in reducing Doppler intermodulation distortion). For what it's worth, what we commonly refer to as "intermodulation distortion" is "amplitude intermodulation distortion" (AIM). Speakers are the only device that I'm aware of that would exhibit measurable Doppler intermodulation distortion, or DIM. o Are horn speakers (including low frequency horns, like Klipschorns) less susceptible to DIM due to the fact that they're more efficient, and require less diaphragm motion for a given SPL? |
#3
|
|||
|
|||
The Ghost wrote:
THE HYPOTHESIS: Assuming that the equation for the Doppler frequency shift of a source moving at constant velocity also applies under dynamically changing velocity conditions, one would expect the propagating sound, that is produced by a high-frequency source moving dynamically at a low frequency around a fixed position, to be frequency modulated. One would further expect that the instantaneous frequency of the propagating sound would reflect the dynamic low-frequency velocity the source. If so, the waveform of the fm-demodulated high-frequency propagating sound, should follow on an instantaneous basis, the dynamic velocity of the low-frequency velocity of the source. major snippage. here we go again. The flaw in this argument is that this set up assumes it is the same as the linear superposition of the of the two signals in a single transducer. it is not. Ian |
#4
|
|||
|
|||
The flaw in this argument is that this set up assumes it is the same as
the linear superposition of the of the two signals in a single transducer. it is not. A single loudspeaker reproducing the linear sum of two different frequencies. The higher frequency "riding" back and forth on the lower frequency. Will that not affect the wavelength of the higher frequency as a function motion of the diaphragm due to the lower frequency, assuming the speed of sound in air remains constant under these conditions? |
#6
|
|||
|
|||
Paul Guy writes:
[...] This applies to narrow band FM (M less than 0.3). How do you know the type of FM here is narrowband? The deviation is dependent on the throw of the cone and the modulating frequency (higher frequencies have a higher first derivative, thus the associated Doppler will be higher) These effects are highly implementation- and signal-specific. Doppler effects can be reduced by 3 way speaker systems, appropriate crossovers, larger cones (less velocity for same sound pressure level). A real-life example of Doppler distortion in woofers in direct-radiator systems can be heard in Emerson, Lake and Palmer's "Trilogy" album (circa 1974?) in which a hellatious low synth bass note is sustained simultaneously with notes from some type of bell(s). The key is that the bell notes have fundamentals that aren't that high - probably under 1 kHz - so they fall within the woofer's range. Most direct-radiator systems produce this passage horribly, especially with any volume. The Klipschorns do a marvelous job. -- % Randy Yates % "So now it's getting late, %% Fuquay-Varina, NC % and those who hesitate %%% 919-577-9882 % got no one..." %%%% % 'Waterfall', *Face The Music*, ELO http://home.earthlink.net/~yatescr |
#7
|
|||
|
|||
"Paul Guy" wrote in message
snip mostly agreeable lead-up comments This applies to narrow band FM (M less than 0.3). Notice that the sign of the lower sideband is the only difference. Because IM distortion is a second or higher order effect, they increase in amplitude more than FM sidebands as the signal increases. The practical way to tell the difference is to look at the amplitude of the microphone signal versus time. Not much help when the modulation indices are low and the measurement environment is noisy, as it always seems to be for speakers. If there is a variation of amplitude (AM modulation), you have IM distortion. Then take your signal and "clip it" (square wave), then look for sidebands. These sidebands will be from the FM or Doppler distortion. A bit more than that. You have to narrowband bandpass filter it before clipping in order to avoid intermodulation. After clipping you either filter it again, or just ignore the out-of band distortion product. In terms of psychoacoustics I don't know if the ear can tell the difference between AM and narrow band FM (Doppler) distortion. My guess is that it can't, since the cochlea cannot determine phase, unless both frequencies are very close (you'll hear "beating"), there will be no way that the hearing system can determine the phase relation. Do tremolo and vibrato sound different? What is most relevant to your discussion, is that in the presence of a loud tone, there is considerable "masking" at frequencies close to the main tone. Roughly speaking, for frequencies from the main tone to about 20% lower, and from the main tone and about 50% higher, the sidebands will not be heard if they are 20 db less than the main tone. The relationship is complicated, in some cases its much less than the 20 db (after Wegal and Lane, 1924). What this really says, is that NEARBY sidebands must be more than 10% before they can be heard in any form. If this is truly the case, Doppler distortion is probably there, but the ear cannot sense it. A bit more than that. If nearby sidebands were that hard to hear, we'd never hear tremolo and vibrato when the modulating frequency is low. There are two modes of perception of modulation. If the sidebands are close to the carrier, and they are audible, they are audible as roughness. If they are distant from the carrier, then they are audible as separate tones, subject to the kind of spectral masking shown above. If you check the sensitivity of the ear to multiple tones, you will find that masking makes many of these forms of distortion into a non-issue. See previous comments about low frequency modulation. snip mostly agreeable other comments |
#8
|
|||
|
|||
"Randy Yates" wrote in message
Paul Guy writes: [...] This applies to narrow band FM (M less than 0.3). How do you know the type of FM here is narrowband? Look at the sidebands. If there is a simple structure and/or they are small, then the modulation index is probably low. The deviation is dependent on the throw of the cone and the modulating frequency (higher frequencies have a higher first derivative, thus the associated Doppler will be higher) These effects are highly implementation- and signal-specific. Yes, note that our experiments cover a range of 40 dB. Doppler effects can be reduced by 3 way speaker systems, appropriate crossovers, larger cones (less velocity for same sound pressure level). A real-life example of Doppler distortion in woofers in direct-radiator systems can be heard in Emerson, Lake and Palmer's "Trilogy" album (circa 1974?) in which a hellatious low synth bass note is sustained simultaneously with notes from some type of bell(s). The key is that the bell notes have fundamentals that aren't that high - probably under 1 kHz - so they fall within the woofer's range. Most direct-radiator systems produce this passage horribly, especially with any volume. The Klipschorns do a marvelous job. How do you know that this isn't just plain old AM distortion? |
#9
|
|||
|
|||
"Arny Krueger" writes:
[...] How do you know that this isn't just plain old AM distortion? It sounds like the bell tones are warbling, i.e., varying in frequency. As a listener, it really doesn't matter, distortion is distortion - the sound is MUCH better with it removed. -- % Randy Yates % "My Shangri-la has gone away, fading like %% Fuquay-Varina, NC % the Beatles on 'Hey Jude'" %%% 919-577-9882 % %%%% % 'Shangri-La', *A New World Record*, ELO http://home.earthlink.net/~yatescr |
#10
|
|||
|
|||
"Arny Krueger" writes:
"Randy Yates" wrote in message [...] The deviation is dependent on the throw of the cone and the modulating frequency (higher frequencies have a higher first derivative, thus the associated Doppler will be higher) These effects are highly implementation- and signal-specific. Yes, note that our experiments cover a range of 40 dB. 40 dB? What exactly is 40 dB? -- % Randy Yates % "Bird, on the wing, %% Fuquay-Varina, NC % goes floating by %%% 919-577-9882 % but there's a teardrop in his eye..." %%%% % 'One Summer Dream', *Face The Music*, ELO http://home.earthlink.net/~yatescr |
#11
|
|||
|
|||
"Randy Yates" wrote in message
"Arny Krueger" writes: "Randy Yates" wrote in message [...] The deviation is dependent on the throw of the cone and the modulating frequency (higher frequencies have a higher first derivative, thus the associated Doppler will be higher) These effects are highly implementation- and signal-specific. Yes, note that our experiments cover a range of 40 dB. 40 dB? What exactly is 40 dB? Sound level intensity. I think the actual SPLs were 78, 88, 98 and 108 dB, more or less @ 1 meter. RS SPL meter so its not excactly NBS tracable, |
#12
|
|||
|
|||
"Arny Krueger" writes:
"Randy Yates" wrote in message "Arny Krueger" writes: "Randy Yates" wrote in message [...] The deviation is dependent on the throw of the cone and the modulating frequency (higher frequencies have a higher first derivative, thus the associated Doppler will be higher) These effects are highly implementation- and signal-specific. Yes, note that our experiments cover a range of 40 dB. 40 dB? What exactly is 40 dB? Sound level intensity. I think the actual SPLs were 78, 88, 98 and 108 dB, more or less @ 1 meter. RS SPL meter so its not excactly NBS tracable, What level was the first plot on your site (the one with the simple 4000 + 50 Hz signal) made at? (Approximate is fine.) Also, as I asked in a personal email, if cone motion does not account for the AM, then how would you account for it? -- % Randy Yates % "The dreamer, the unwoken fool - %% Fuquay-Varina, NC % in dreams, no pain will kiss the brow..." %%% 919-577-9882 % %%%% % 'Eldorado Overture', *Eldorado*, ELO http://home.earthlink.net/~yatescr |
#13
|
|||
|
|||
Karl Uppiano wrote:
The flaw in this argument is that this set up assumes it is the same as the linear superposition of the of the two signals in a single transducer. it is not. A single loudspeaker reproducing the linear sum of two different frequencies. The higher frequency "riding" back and forth on the lower frequency. Will that not affect the wavelength of the higher frequency as a function motion of the diaphragm due to the lower frequency, assuming the speed of sound in air remains constant under these conditions? Go look in a good text book for the words 'linear' and 'sum' Ian |
#14
|
|||
|
|||
"ruffrecords" wrote in message ... Karl Uppiano wrote: The flaw in this argument is that this set up assumes it is the same as the linear superposition of the of the two signals in a single transducer. it is not. A single loudspeaker reproducing the linear sum of two different frequencies. The higher frequency "riding" back and forth on the lower frequency. Will that not affect the wavelength of the higher frequency as a function motion of the diaphragm due to the lower frequency, assuming the speed of sound in air remains constant under these conditions? Go look in a good text book for the words 'linear' and 'sum' Why don't you just answer my question, and forego the superior attitude? I'm sure you can figure out what I meant. |
#15
|
|||
|
|||
"Randy Yates" wrote in message
"Arny Krueger" writes: "Randy Yates" wrote in message "Arny Krueger" writes: "Randy Yates" wrote in message [...] The deviation is dependent on the throw of the cone and the modulating frequency (higher frequencies have a higher first derivative, thus the associated Doppler will be higher) These effects are highly implementation- and signal-specific. Yes, note that our experiments cover a range of 40 dB. 40 dB? What exactly is 40 dB? Sound level intensity. I think the actual SPLs were 78, 88, 98 and 108 dB, more or less @ 1 meter. RS SPL meter so its not excactly NBS tracable, What level was the first plot on your site (the one with the simple 4000 + 50 Hz signal) made at? (Approximate is fine.) About 90 dN at one meter. Also, as I asked in a personal email, if cone motion does not account for the AM, then how would you account for it? Speakers being speakers! ;-) |
#16
|
|||
|
|||
Karl Uppiano wrote:
"ruffrecords" wrote in message ... Karl Uppiano wrote: The flaw in this argument is that this set up assumes it is the same as the linear superposition of the of the two signals in a single transducer. it is not. A single loudspeaker reproducing the linear sum of two different frequencies. The higher frequency "riding" back and forth on the lower frequency. Will that not affect the wavelength of the higher frequency as a function motion of the diaphragm due to the lower frequency, assuming the speed of sound in air remains constant under these conditions? Go look in a good text book for the words 'linear' and 'sum' Why don't you just answer my question, and forego the superior attitude? I'm sure you can figure out what I meant. OK. No, otherwise it would not be a linear sum. Hence my reading suggestion. Ian |
#17
|
|||
|
|||
"ruffrecords" wrote in message ... Karl Uppiano wrote: "ruffrecords" wrote in message ... Karl Uppiano wrote: The flaw in this argument is that this set up assumes it is the same as the linear superposition of the of the two signals in a single transducer. it is not. A single loudspeaker reproducing the linear sum of two different frequencies. The higher frequency "riding" back and forth on the lower frequency. Will that not affect the wavelength of the higher frequency as a function motion of the diaphragm due to the lower frequency, assuming the speed of sound in air remains constant under these conditions? Go look in a good text book for the words 'linear' and 'sum' Why don't you just answer my question, and forego the superior attitude? I'm sure you can figure out what I meant. OK. No, otherwise it would not be a linear sum. Hence my reading suggestion. I understand what "linear" and "sum" mean. When modulated by two sinusoids, the x position of the diaphragm as a function of time is defined by x( t ) = A sin( w1 t ) + B sin( w2 t ) Where A and B are the amplitudes of the two frequencies, and w2 and w2 are the frequencies in radians per second of the two frequencies. Let's call w1 the low frequency and w2 the high frequency. There are no non-linear terms in this equation, so we won't get harmonic or IM distortion. I understand that. Since Doppler shift is based on the velocity, not the position of the diaphragm, we must differentiate this equation. The velocity of the diaphragm as a function of time is then v( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t ) The formula for Doppler shift is ls = lo ( 1 - ( vs / c ) ) where ls = the resulting wavelength (lambda shifted) lo = the original wavelength of the higher frequency (lambda original) vs = the velocity of the source (diaphragm velocity) c = is the speed of sound in air therefore, substituting v(t) for vs, ls( t ) = lo ( 1 - ( ( w1 A cos( w1 t ) + w2 B cos( w2 t ) ) / c ) ) which appears to my eye as a time-varying wavelength based on the diaphragm velocity. What am I doing wrong? |
#18
|
|||
|
|||
"ruffrecords" wrote in message ... Karl Uppiano wrote: "ruffrecords" wrote in message ... Karl Uppiano wrote: The flaw in this argument is that this set up assumes it is the same as the linear superposition of the of the two signals in a single transducer. it is not. A single loudspeaker reproducing the linear sum of two different frequencies. The higher frequency "riding" back and forth on the lower frequency. Will that not affect the wavelength of the higher frequency as a function motion of the diaphragm due to the lower frequency, assuming the speed of sound in air remains constant under these conditions? Go look in a good text book for the words 'linear' and 'sum' Why don't you just answer my question, and forego the superior attitude? I'm sure you can figure out what I meant. OK. No, otherwise it would not be a linear sum. Hence my reading suggestion. Reposting this, since it didn't appear to "take" last time: I understand what "linear" and "sum" mean. When modulated by two sinusoids, the x position of the diaphragm as a function of time is defined by x( t ) = A sin( w1 t ) + B sin( w2 t ) Where A and B are the amplitudes of the two frequencies, and w2 and w2 are the frequencies in radians per second of the two frequencies. Let's call w1 the low frequency and w2 the high frequency. There are no non-linear terms in this equation, so we won't get harmonic or IM distortion. I understand that. Since Doppler shift is based on the velocity, not the position of the diaphragm, we must differentiate this equation. The velocity of the diaphragm as a function of time is then v( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t ) The formula for Doppler shift is ls = lo ( 1 - ( vs / c ) ) where ls = the resulting wavelength (lambda shifted) lo = the original wavelength of the higher frequency (lambda original) vs = the velocity of the source (diaphragm velocity) c = is the speed of sound in air therefore, substituting v(t) for vs, ls( t ) = lo ( 1 - ( ( w1 A cos( w1 t ) + w2 B cos( w2 t ) ) / c ) ) which appears to my eye as a time-varying wavelength based on the diaphragm velocity. What am I doing wrong? |
#19
|
|||
|
|||
Karl Uppiano wrote: I understand what "linear" and "sum" mean. When modulated by two sinusoids, the x position of the diaphragm as a function of time is defined by x( t ) = A sin( w1 t ) + B sin( w2 t ) It is the piston velocity v(t) that follows this for equal sound pressure at all frequencies. Where A and B are the amplitudes of the two frequencies, and w2 and w2 are the frequencies in radians per second of the two frequencies. Let's call w1 the low frequency and w2 the high frequency. There are no non-linear terms in this equation, so we won't get harmonic or IM distortion. I understand that. Since Doppler shift is based on the velocity, not the position of the diaphragm, we must differentiate this equation. The velocity of the diaphragm as a function of time is then v( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t ) That would be the acceleration a(t) which has no acoustic consequences. I'm too tired right now to follow those corrections all the way through the rest of your welcome attempt to quantify this but would you consider working them through to the conclusion you can reach? Thanks, Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#20
|
|||
|
|||
"Bob Cain" wrote in message ... Karl Uppiano wrote: I understand what "linear" and "sum" mean. When modulated by two sinusoids, the x position of the diaphragm as a function of time is defined by x( t ) = A sin( w1 t ) + B sin( w2 t ) It is the piston velocity v(t) that follows this for equal sound pressure at all frequencies. Hmmm... what is the equation for x( t ) then? Where A and B are the amplitudes of the two frequencies, and w2 and w2 are the frequencies in radians per second of the two frequencies. Let's call w1 the low frequency and w2 the high frequency. There are no non-linear terms in this equation, so we won't get harmonic or IM distortion. I understand that. Since Doppler shift is based on the velocity, not the position of the diaphragm, we must differentiate this equation. The velocity of the diaphragm as a function of time is then v( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t ) That would be the acceleration a(t) which has no acoustic consequences. Isn't velocity the first derivative of position? Isn't acceleration the first derivative of velocity? It seems that acceleration (if we cared about it) would be a( t ) = - ( w1^2 A sin( w1 t ) + w2^2 B sin( w2 t ) ) However, all three equations only differ by a constant. So I believe you could get the same physical consequences by simply adjusting A and B accordingly. I'm too tired right now to follow those corrections all the way through the rest of your welcome attempt to quantify this but would you consider working them through to the conclusion you can reach? My end result would differ by a constant (i.e., it would have a different magnitude), as I mentioned above, but I believe the phenomenon would be the same. Thanks, Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#21
|
|||
|
|||
Karl Uppiano wrote: "Bob Cain" wrote in message ... Karl Uppiano wrote: I understand what "linear" and "sum" mean. When modulated by two sinusoids, the x position of the diaphragm as a function of time is defined by x( t ) = A sin( w1 t ) + B sin( w2 t ) It is the piston velocity v(t) that follows this for equal sound pressure at all frequencies. Hmmm... what is the equation for x( t ) then? x( t ) = -(A/w1) cos( w1 t ) - (B/w2) cos( w2 t ) Isn't velocity the first derivative of position? Isn't acceleration the first derivative of velocity? It seems that acceleration (if we cared about it) would be a( t ) = - ( w1^2 A sin( w1 t ) + w2^2 B sin( w2 t ) ) Try a( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t ) However, all three equations only differ by a constant. So I believe you could get the same physical consequences by simply adjusting A and B accordingly. And phase. The adjustment to A and B is a constant if W is. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#22
|
|||
|
|||
"Bob Cain" wrote in message ... Karl Uppiano wrote: "Bob Cain" wrote in message ... Karl Uppiano wrote: I understand what "linear" and "sum" mean. When modulated by two sinusoids, the x position of the diaphragm as a function of time is defined by x( t ) = A sin( w1 t ) + B sin( w2 t ) It is the piston velocity v(t) that follows this for equal sound pressure at all frequencies. Hmmm... what is the equation for x( t ) then? x( t ) = -(A/w1) cos( w1 t ) - (B/w2) cos( w2 t ) ....which I assume you arrived at by integrating my original equation. Is there a derivation of this somewhere that I can look up? Isn't velocity the first derivative of position? Isn't acceleration the first derivative of velocity? It seems that acceleration (if we cared about it) would be a( t ) = - ( w1^2 A sin( w1 t ) + w2^2 B sin( w2 t ) ) Try a( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t ) However, all three equations only differ by a constant. So I believe you could get the same physical consequences by simply adjusting A and B accordingly. And phase. The adjustment to A and B is a constant if W is. Right. Bottom line, though, it seems that the wavelength is still a time-varying function of the diaphragm velocity. Now, I need to understand how the diaphragm motion is converted into sound. I will accept the possibility that somehow the motion is irrelevant to the wavelength, but I need to see the physics. |
#23
|
|||
|
|||
Karl Uppiano wrote: "Bob Cain" wrote in message ... Karl Uppiano wrote: "Bob Cain" wrote in message ... Karl Uppiano wrote: I understand what "linear" and "sum" mean. When modulated by two sinusoids, the x position of the diaphragm as a function of time is defined by x( t ) = A sin( w1 t ) + B sin( w2 t ) It is the piston velocity v(t) that follows this for equal sound pressure at all frequencies. Hmmm... what is the equation for x( t ) then? x( t ) = -(A/w1) cos( w1 t ) - (B/w2) cos( w2 t ) ...which I assume you arrived at by integrating my original equation. Is there a derivation of this somewhere that I can look up? Yes. I just noted that for frequency independant operation it is the velocity that should have been modeled with your equation, not the position. x( t ) and a( t ) follow by differentiation and integration respectively. And phase. The adjustment to A and B is a constant if W is. Right. Bottom line, though, it seems that the wavelength is still a time-varying function of the diaphragm velocity. Why would the wavelength vary over time? If you drive the piston with a fixed magnitude sinusoid, its wavelength is fixed and so is that of the acoustic wave it puts out unless it moves with constant velocity relative to the air. If driven with any periodic function, the period is determined by the lowest Fourier component. The velocity of that piston is converted into an acoustic wave with the same shape as that of the piston's velocity function. If it is in constant linear translation, the wave function will be an expanded or contracted version of the piston's velocity function. That's Doppler shift. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#24
|
|||
|
|||
"Bob Cain" wrote in message ... Karl Uppiano wrote: "Bob Cain" wrote in message ... Karl Uppiano wrote: "Bob Cain" wrote in message ... Karl Uppiano wrote: I understand what "linear" and "sum" mean. When modulated by two sinusoids, the x position of the diaphragm as a function of time is defined by x( t ) = A sin( w1 t ) + B sin( w2 t ) It is the piston velocity v(t) that follows this for equal sound pressure at all frequencies. Hmmm... what is the equation for x( t ) then? x( t ) = -(A/w1) cos( w1 t ) - (B/w2) cos( w2 t ) ...which I assume you arrived at by integrating my original equation. Is there a derivation of this somewhere that I can look up? Yes. I just noted that for frequency independant operation it is the velocity that should have been modeled with your equation, not the position. x( t ) and a( t ) follow by differentiation and integration respectively. And phase. The adjustment to A and B is a constant if W is. Right. Bottom line, though, it seems that the wavelength is still a time-varying function of the diaphragm velocity. Why would the wavelength vary over time? If you drive the piston with a fixed magnitude sinusoid, its wavelength is fixed and so is that of the acoustic wave it puts out unless it moves with constant velocity relative to the air. If driven with any periodic function, the period is determined by the lowest Fourier component. The velocity of that piston is converted into an acoustic wave with the same shape as that of the piston's velocity function. If it is in constant linear translation, the wave function will be an expanded or contracted version of the piston's velocity function. That's Doppler shift. Is there a web site that would describe the physics, mathematically, of how diaphragm motion is converted to sound? And more specifically, with two frequencies, how the time-varying velocity of the lower frequency would not Doppler-shift the higher one? I just want to understand the physics of this, and get at the truth of the matter. |
#25
|
|||
|
|||
Karl Uppiano wrote: Is there a web site that would describe the physics, mathematically, of how diaphragm motion is converted to sound? If you are up to it: http://www.silcom.com/~aludwig/Physi..._of_sound.html I haven't printed it off and holed up with it yet and I've got to do that. And more specifically, with two frequencies, how the time-varying velocity of the lower frequency would not Doppler-shift the higher one? I just want to understand the physics of this, and get at the truth of the matter. The piston doesn't know from two frequencies. It knows and transfers its instantaneous velocity to the correct position of the outward propegating wave. It doesn't care what was mixed to get that velocity and it doesn't care what came before or after that instant. If you can make the piston move the way you want you can get it to produce the acoustic wave you want. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#26
|
|||
|
|||
On Tue, 17 Aug 2004 00:21:59 -0700, Bob Cain
wrote: Karl Uppiano wrote: I understand what "linear" and "sum" mean. When modulated by two sinusoids, the x position of the diaphragm as a function of time is defined by x( t ) = A sin( w1 t ) + B sin( w2 t ) It is the piston velocity v(t) that follows this for equal sound pressure at all frequencies. Oops a daisy! |
#27
|
|||
|
|||
"The Ghost" wrote in message om... THE HYPOTHESIS: Assuming that the equation for the Doppler frequency shift of a source moving at constant velocity also applies under dynamically changing velocity conditions, one would expect the propagating sound, that is produced by a high-frequency source moving dynamically at a low frequency around a fixed position, to be frequency modulated. One would further expect that the instantaneous frequency of the propagating sound would reflect the dynamic low-frequency velocity the source. If so, the waveform of the fm-demodulated high-frequency propagating sound, should follow on an instantaneous basis, the dynamic velocity of the low-frequency velocity of the source. THE SETUP: A small circular piezoelectric bimorph, having a resonant frequency of approximately 10KHz was attached to the 10-lb armature/shaft of a linear motor. The displacement of the armature/shaft was monitored by a linear displacement transducer attached to the opposite end of the armature/shaft. The linear displacement transducer also provided feedback for the servo amplifier which was driving the linear motor. Because the linear motor was in a servo loop, the displacement of the motor followed with reasonable accuracy both sinusoidal and non-sinusoidal command signals that were applied to the amplifier. The piezoelectric sound source was driven by a low-distortion oscillator at 10KHz. The sound emitted by the source was measured by a microphone at a distance of approximately one foot. The output of the microphone was amplified, high-pass filtered and applied to a frequency-to-voltage converter. The output of the frequency-to-voltage converter was low-pass filtered to reduce the level of the residual 10KHz carrier, amplified and applied to a signal averager. The signal averager was triggered by the command signal that was applied to the linear motor. Averaging was used in order to remove non-coherent 60Hz that was present in the output of the demodulator. THE MOTION OF THE SOUND SOURCE A triangular command signal having a 50-msec period was applied to the servo amplifier. A triangular command signal was used in order to simplify interpretation of the measurement result and to avoid the phase shift vs time delay ambiguity that would otherwise exist with fixed frequency sinusoidal excitation. The output of the displacement transducer was monitored on an oscilloscope and found to be triangular with rounded corners. The rounding of the corners is due to the limited closed-bandwidth of the servo. The velocity of the linear motor was therefore trapezoidal with relatively flat and relatively long plateaus and relatively short transitions. THE MEASUREMENT RESULT The propagating 10KHz signal emitted by the piezo bimorph was applied to an FFT analyzer in zoom-analysis mode with a resolution bandwidth of 0.1Hz. When the piezo bimorph was stationary, the propagating signal picked up by the microphone showed only a single spectral peak at 10KHz. When the piezo transducer was moving back and forth with a triangular displacement provided by the linear motor, the propagating signal received by the microphone contained numerous sidebands which were indicative of FM modulation. Additionally, the output of the FM demodulator was observed to be trapezoidal and followed on an instantaneous basis the velocity of the linear motor and the attached piezo transducer. THE CHALLENGE In science, theory usually follows experimental results. In this case the experimental result shows that a 10KHz signal applied to a small piezoelectric source moving back and forth around a fixed position becomes frequency modulated by the back and forth motion of the source. The measurement further shows that the received, FM-demodulated signal follows the instantaneous velocity of the source. This result is exactly what is expected on the basis of Doppler frequency shift extrapolated from constant velocity to dynamic velocity conditions. While some might argue that the observed FM-like sidebands and the trapezoidal demodulated waveform are the result of IM distortion, and not Doppler FM, the ball is in their court. It is now up to them to provide an explanation/analysis involving an IM producing mechanism in the present experimental setup that accounts for the present experimental result. Finally, it must be noted that the purpose of the present measurement was to demonstrate fundamental phenomenological behavior. The 10KHz carrier and the 50-msec peridiocity for the displacement of the linear motor were chosen solely to accommodate the hardware on hand. There is presently no reason to believe that the outcome of the present measurement would be different if other carrier frequencies or other source displacement periodicities or waveshapes were used. Since this thread was started, it has meandered here and there, and I just realized that we may have jumped to some invalid conclusions. Here are some important points to consider: 1. I believe this experiment is relevant in that we should be able to mathematically predict and experimentally measure frequency modulation due to Doppler shifts with a good degree of agreement within the constraints this setup (i.e., a linear motor pushing a peizo radiator back and forth). It is not clear whether the OP was able to correlate the experimental results with the mathematical predictions, or merely *detected something*. There may be some more work required here. 2. This experiment *cannot* be generalized to mathematically predict and experimentally measure frequency modulation due to Doppler shifts *through a loudspeaker*. Note that the experiment doesn't mention this generalization; it does not discuss loudspeakers at all. The linear motor does *not* radiate the low frequency as sound waves, as a loudspeaker does. This completely changes the dynamics of the situation in terms of the motion of the radiators and the transfer of energy into the surrounding air. 3. To have any relevance to audio reproduction through loudspeakers, this experiment needs to be repeated to mathematically predict, and then, *using a loudspeaker*, experimentally measure frequency modulation due to Doppler shifts. 4. For either experiment, it is not sufficient to simply *detect* FM sidebands. The frequencies, amplitudes and phases obtained experimentally must agree closely with the values predicted mathematically. |
#28
|
|||
|
|||
"Karl Uppiano" wrote in message ...
"The Ghost" wrote in message om... THE HYPOTHESIS: Assuming that the..... THE SETUP: A small circular piezoelectric bimorph....... THE MOTION OF THE SOUND SOURCE A triangular command signal......... THE MEASUREMENT RESULT The propagating 10KHz signal....... THE CHALLENGE In science, theory usually follows......... 1. I believe this experiment is relevant in that we should be able to mathematically predict and experimentally measure frequency modulation due to Doppler shifts with a good degree of agreement within the constraints this setup (i.e., a linear motor pushing a peizo radiator back and forth). It is not clear whether the OP was able to correlate the experimental results with the mathematical predictions, or merely *detected something*. There may be some more work required here. You are correct. You should be able to mathematically model the experiment and predict the experimental result, but I am not going to do it for you. Also, the measurement didn't just merely detect "something." The measurement demonstrated that motional information about the periodic trapezoidal velocity the peizo element exists in the FM sidebands of the 10KHz propagating carrier and that the FM demodulated signal had the same trapezoidal shape as the velocity of the shaft of the linear motor. This result is exactly what is predicted qualitatively by a phenomenological model of dynamic Doppler shift. This experimental result is difficult, if not impossible, to explain on the basis of IM distortion because there is no readily identifiable nonlinear mechanism that is common to both the low-frequency motion of the shaft and the high frequency motion of the piezo element. The measurement results provide a very strong counter-argument against those claiming that dynamic Doppler shift does not exist. That was the sole purpose of measurement. If you or anyone else wishes to carry it to the next "quantative" level, please be my guest. 2. This experiment *cannot* be generalized to mathematically predict and experimentally measure frequency modulation due to Doppler shifts *through a loudspeaker*. Note that the experiment doesn't mention this generalization; it does not discuss loudspeakers at all. That is correct, unless you can find a loudspeaker that produces negligible IM distortion so that the propagating energy in the sidebands is predominantly the result of dynamic Doppler shift and not the result of IM in the actual cone vibration itself. The linear motor does *not* radiate the low frequency as sound waves, as a loudspeaker does. This completely changes the dynamics of the situation in terms of the motion of the radiators and the transfer of energy into the surrounding air. That is incorrect. The surface of the piezo element radiates the low frequency motion of the motor shaft, but that radiation is very low because the frequency is low and because the surface area of the piezo element is small. Furthermore, the amount of low-frequency sound that is radiated is irrelevent to the issue of the production of dynamic Doppler shift. 3. To have any relevance to audio reproduction through loudspeakers, this experiment needs to be repeated to mathematically predict, and then, *using a loudspeaker*, experimentally measure frequency modulation due to Doppler shifts. Because of the existence of IM, the mathematical model will have to take into account both the radiation of IM products as well as the dynamic Doppler shift, since both contribute sideband energy at the same frequencies. If you are prepared to take on that task, all I can do is wish you luck. 4. For either experiment, it is not sufficient to simply *detect* FM sidebands. The frequencies, amplitudes and phases obtained experimentally must agree closely with the values predicted mathematically. Amplitudes and phase information needs to be preserved, but in the case of my experiment, no mathematical prediction is necessary. I used a trapezoidal instead of sinusoidal velocity of the shaft linear motor specifically to get around the need for a mathematical prediction. Because the velocity of the linear motor was non-sinusoidal, the information in the sidebands needs to be accurate only in terms of relative amplitude and relative phase. The non-sinusoidal velocity information will be preserved in the sidebands, and appear at the output of the FM demodulator, only if the relative ampliude and relative phase information is correctly preserved in the sidebands of the radiated signal. |
#29
|
|||
|
|||
"The Ghost" wrote in message om... "Karl Uppiano" wrote in message ... "The Ghost" wrote in message om... THE HYPOTHESIS: Assuming that the..... THE SETUP: A small circular piezoelectric bimorph....... THE MOTION OF THE SOUND SOURCE A triangular command signal......... THE MEASUREMENT RESULT The propagating 10KHz signal....... THE CHALLENGE In science, theory usually follows......... 1. I believe this experiment is relevant in that we should be able to mathematically predict and experimentally measure frequency modulation due to Doppler shifts with a good degree of agreement within the constraints this setup (i.e., a linear motor pushing a peizo radiator back and forth). It is not clear whether the OP was able to correlate the experimental results with the mathematical predictions, or merely *detected something*. There may be some more work required here. You are correct. You should be able to mathematically model the experiment and predict the experimental result, but I am not going to do it for you. Also, the measurement didn't just merely detect "something." The measurement demonstrated that motional information about the periodic trapezoidal velocity the peizo element exists in the FM sidebands of the 10KHz propagating carrier and that the FM demodulated signal had the same trapezoidal shape as the velocity of the shaft of the linear motor. This result is exactly what is predicted qualitatively by a phenomenological model of dynamic Doppler shift. This experimental result is difficult, if not impossible, to explain on the basis of IM distortion because there is no readily identifiable nonlinear mechanism that is common to both the low-frequency motion of the shaft and the high frequency motion of the piezo element. The measurement results provide a very strong counter-argument against those claiming that dynamic Doppler shift does not exist. That was the sole purpose of measurement. If you or anyone else wishes to carry it to the next "quantative" level, please be my guest. That's why my initial reaction to your experiment was positive. My mistake (and others also) was in jumping to the conclusion that your results could be applied directly to Doppler FM in a loudspeaker. It cannot, and you never claimed they could, which is a "Good Thing". 2. This experiment *cannot* be generalized to mathematically predict and experimentally measure frequency modulation due to Doppler shifts *through a loudspeaker*. Note that the experiment doesn't mention this generalization; it does not discuss loudspeakers at all. That is correct, unless you can find a loudspeaker that produces negligible IM distortion so that the propagating energy in the sidebands is predominantly the result of dynamic Doppler shift and not the result of IM in the actual cone vibration itself. Unfortunately, that's true. AM and FM sidebands look fairly similar at low FM modulation indices. They might be hard to distinguish, although IIRC, upper and lower FM sidebands are opposite in phase. The linear motor does *not* radiate the low frequency as sound waves, as a loudspeaker does. This completely changes the dynamics of the situation in terms of the motion of the radiators and the transfer of energy into the surrounding air. That is incorrect. The surface of the piezo element radiates the low frequency motion of the motor shaft, but that radiation is very low because the frequency is low and because the surface area of the piezo element is small. Furthermore, the amount of low-frequency sound that is radiated is irrelevent to the issue of the production of dynamic Doppler shift. The low frequency radiation is much less efficient for the reasons you state. A loudspeaker, on the other hand, radiates all frequencies in its usable frequency range with nominally equal efficiency. That is not the case with your experimental setup, as you point out. I not only believe that it is not only relevant, *but crucial* whether the low frequency component is radiated, to the issue of dynamic Doppler shift. The entire energy equation changes. Instead of a high frequency sound source moving back and forth in free air, we are instead summing two acoustic waves. It's entirely different. 3. To have any relevance to audio reproduction through loudspeakers, this experiment needs to be repeated to mathematically predict, and then, *using a loudspeaker*, experimentally measure frequency modulation due to Doppler shifts. Because of the existence of IM, the mathematical model will have to take into account both the radiation of IM products as well as the dynamic Doppler shift, since both contribute sideband energy at the same frequencies. If you are prepared to take on that task, all I can do is wish you luck. I'm afraid I don't have the time or the equipment. I'm just suggesting the need for further research if anyone is really interested in proving or disproving the existence of Doppler FM in loudspeakers. This is where a prediction from a mathematical model is important. It isn't sufficient to get a louspeaker to produce something that "smells like Doppler FM". You need a model that predicts how much, at what freqencies, in what phase, etc., and then you need to get good experimental agreement with your prediction. Otherwise, you could be measuring anything -- other forms of distortion, environmental noise, sampling errors, etc. In the end, it must all be accounted for if it's the *truth* you're looking for. Unsubstantiated claims are much less demanding :-) 4. For either experiment, it is not sufficient to simply *detect* FM sidebands. The frequencies, amplitudes and phases obtained experimentally must agree closely with the values predicted mathematically. Amplitudes and phase information needs to be preserved, but in the case of my experiment, no mathematical prediction is necessary. I used a trapezoidal instead of sinusoidal velocity of the shaft linear motor specifically to get around the need for a mathematical prediction. Because the velocity of the linear motor was non-sinusoidal, the information in the sidebands needs to be accurate only in terms of relative amplitude and relative phase. The non-sinusoidal velocity information will be preserved in the sidebands, and appear at the output of the FM demodulator, only if the relative ampliude and relative phase information is correctly preserved in the sidebands of the radiated signal. I believe prediction *is* necessary. You did predict some things, and you were able to experimentally bear out your predictions. But if you had predicted trapezoidal FM with a slope x, and you measured sinusoidal FM with a maximum slope of -2x, I'd say your predictions, or your measurements were off. You haven't proved anything until you have a high degree of agreement between your prediction and your measured results, and you can account for any remaining errors to the satisfaction of all reviewers. That's what's meant by "reproducible results". |
#30
|
|||
|
|||
The Ghost wrote: The linear motor does *not* radiate the low frequency as sound waves, as a loudspeaker does. This completely changes the dynamics of the situation in terms of the motion of the radiators and the transfer of energy into the surrounding air. That is incorrect. The surface of the piezo element radiates the low frequency motion of the motor shaft, but that radiation is very low because the frequency is low and because the surface area of the piezo element is small. Furthermore, the amount of low-frequency sound that is radiated is irrelevent to the issue of the production of dynamic Doppler shift. He was correct and you are not. It is entirely a matter of the frequency dependant coupling. I know, I know. You could prove otherwise but won't. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#31
|
|||
|
|||
"Karl Uppiano" wrote in message .. .
That's why my initial reaction to your experiment was positive. My mistake (and others also) was in jumping to the conclusion that your results could be applied directly to Doppler FM in a loudspeaker. It cannot, and you never claimed they could, which is a "Good Thing". My measurement results can be applied to a loudspeaker but only to the extent that they demonstrate that dynamic Doppler shift can be produced by a loudspeaker. Whether or not Doppler shift produced by a loudspeaker can be measured is another issue. That is going to depend on the relative amount of intermodulation distortion that the loudspeaker also produces because the Doppler FM components and the intermodulation distortion components are at the same frequencies. Personally, I wouldn't waste my time trying to separate the two. ................... AM and FM sidebands look fairly similar at low FM modulation indices. They might be hard to distinguish, although IIRC, upper and lower FM sidebands are opposite in phase. The FM demodulator that I used was a precision frequency-to-voltage converter which operates on zero crossings and, as such, is completely insensitive to amplitude variations of the signal being demodulated. The low frequency radiation is much less efficient for the reasons you state. A loudspeaker, on the other hand, radiates all frequencies in its usable frequency range with nominally equal efficiency. That is not the case with your experimental setup, as you point out. I not only believe that it is not only relevant, *but crucial* whether the low frequency component is radiated, to the issue of dynamic Doppler shift. The entire energy equation changes. Instead of a high frequency sound source moving back and forth in free air, we are instead summing two acoustic waves. It's entirely different. .............. It isn't sufficient to get a louspeaker to produce something that "smells like Doppler FM". You need a model that predicts how much, at what freqencies, in what phase, etc., and then you need to get good experimental agreement with your prediction. Otherwise, you could be measuring anything -- other forms of distortion, environmental noise, sampling errors, etc. In the end, it must all be accounted for if it's the *truth* you're looking for. Unsubstantiated claims are much less demanding :-) Not surprisingly, we again mostly disagree. In the early stages of research, where the issue is whether or not a phenomenon exists, the first order of business is to demonstrate experimentally the existence of the phenomenon. After the existence of the phenomenon has been demonstrated, model development and quantative predictions follow. For whatever reason, you seem to refuse to distinguish between the existence of a phenomenon and the accurate quantitative description of a phenomenon. The absence of a quantitative description of a phenomenon is not a justifiable excuse for denying its existence. In the history of science, there are many phenomena that were demonstrated first and quantified later. You haven't proved anything until you have a high degree of agreement between your prediction and your measured results, and you can account for any remaining errors to the satisfaction of all reviewers. That's what's meant by "reproducible results". If you believe that, then you have a lot to learn. It has been my experience over many years that models go up in flames, more often than not, becasue of fundamental phenomenological inconsistencies/inadequacies rather than because they did not produce a sufficiently high degree of agreement between prediction and measured results. |
#32
|
|||
|
|||
The Ghost wrote: Not surprisingly, we again mostly disagree. In the early stages of research, where the issue is whether or not a phenomenon exists, the first order of business is to demonstrate experimentally the existence of the phenomenon. After the existence of the phenomenon has been demonstrated, model development and quantative predictions follow. For whatever reason, you seem to refuse to distinguish between the existence of a phenomenon and the accurate quantitative description of a phenomenon. The absence of a quantitative description of a phenomenon is not a justifiable excuse for denying its existence. In the history of science, there are many phenomena that were demonstrated first and quantified later. Evidence for existence of a phenomenon requires elimination of spurious causes one way or another, either by experimental setup or by having a _good_ characterization of the spurious phenomena so that their effect can be removed from the test data. How does your "experiment" do either so that what remains can be legitimately regarded as evidence of Doppler distortion? And even if it satisfied that requirement, the phenomenon in question now is not simply Doppler distortion but the mechanism that produces it so a predictive model is absolutely required. Why, if the mechanism is as simple as is described, has no such model been forthcoming? This is basic stuff and should not have to be spoon fed to anyone who claims to be an experimental scientist. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#33
|
|||
|
|||
Deleting alt.sci.physics.acoustics from the crosspost.
In alt.music.home-studio,rec.audio.tech,rec.audio.pro,alt.sci.physic s.acoustics On Mon, 23 Aug 2004 18:55:28 -0700, Bob Cain wrote: The Ghost wrote: Not surprisingly, we again mostly disagree. In the early stages of research, where the issue is whether or not a phenomenon exists, the first order of business is to demonstrate experimentally the existence of the phenomenon. After the existence of the phenomenon has been demonstrated, model development and quantative predictions follow. For whatever reason, you seem to refuse to distinguish between the existence of a phenomenon and the accurate quantitative description of a phenomenon. The absence of a quantitative description of a phenomenon is not a justifiable excuse for denying its existence. In the history of science, there are many phenomena that were demonstrated first and quantified later. Evidence for existence of a phenomenon requires elimination of spurious causes one way or another, either by experimental setup or by having a _good_ characterization of the spurious phenomena so that their effect can be removed from the test data. How would something cause the doppler effect? By emitting sound and moving relative to a receiver. What is moving (and emitting sound) in the systems we have been describing? Voice coil, cone, spider, surround. Of these, perhaps the surround could cause spurious doppler effect (because it's moving, but "on average" it moves only half as fast and half as far as the cone). It also has much less radiating area than the cone. I'm not even considering the spider and voice coil, because not only do they not offer much surface area, they're not facing forward and aren't 'visible' through the cone. There's also the dust cap, but it is considered part of the cone. You could argue the speaker frame moves in response to the cone's movement (Newton's Nth law of motion, I forget what N is), but that can be reduced substantially by securely mounting the driver on a large concrete block, effectively increasing its mass and lowering its movement. How does your "experiment" do either so that what remains can be legitimately regarded as evidence of Doppler distortion? And even if it satisfied that requirement, the phenomenon in question now is not simply Doppler distortion but the mechanism that produces it so a predictive model is absolutely required. Why, if the mechanism is as simple as is described, has no such model been forthcoming? This is basic stuff and should not have to be spoon fed to anyone who claims to be an experimental scientist. Yes, Bob, it IS basic stuff. The speed of sound at sea level is about 1116 feet per second (google). A 1kHz tone has a wavelenth of 1.116 feet (or 1 foot, 1.32 inches). Run a 1kHz tone from a signal generator into both an oscilloscope (channel 1, trigger on channel 1) and an audio amplifier that drives a speaker. Put a microphone a couple of feet from the speaker, run its output through a preamp (or directly) to channel 2 of the oscilloscope. Adjust vertical gains appropriately to get a good vertical displacement of each sine wave. You should be able, by changing the distance from the microphone to the speaker, put these two sine waves in phase. If you increase the distance between the mic and speaker, the bottom (channel 2) trace should go through a whole cycle when the distance changes by 1 foot and 1.32 inches. Mount the speaker on a shaker table, and program it to do various movements (changing the distance between it and the mic) at various speeds. Observe the scope traces while this is happening. The bottom trace shows a phase change that corresponds exactly and instantly (less a small amount of latency caused by the speed of sound) to the motion of the speaker, or more specifically, the distance between it and the mic. Mix (in the audio, additive sense, not the radio/RF, multiplicative/nonlinear sense) a low-frequency (0.1 Hz to 50 Hz) signal with the 1kHz tone so that they both are amplified and drive the speaker. This causes cone motion (assuming it stays within the linear range of the driver), but the 1kHz signal is still emitted from the speaker. Observe the trace on channel 2, it will show a small amount of phase shift that directly follows the cone motion. Assuming 1/2 inch peak-to-peak cone excursion, the shift in degrees will be 360*(0.5/12)/1.116=13 degrees. This is not a lot, but you should be able to increase both the trace speed (shorter timebase) and the vertical gain for channel 2, and see a diagonal line (if not visible, move the mic until itiis) that moves back and forth with the speaker cone. This movement directly follows the cone motion (which in this case is caused by the low-frequency driving signal), just as it did when the speaker was on the shaker table. Bob, I expect you believe the shaker table description, so you shouldn't have to actually do it. But I would hope you do the description in the last paragraph. I presume you have the equipment to do it and know how to wire it up. You should be able to see the phase change of the 1kHz signal, and IIRC the derivative of the phase change is frequency change. So if the cone moves (actually accelerates or decelerates) a visible distance, it will happen. It doesn't matter if it's below (the cone's free-air) resonance or above resonance, if it moves visibly, it's enough to cause measurable phase shift and thus frequency modulation. Bob I can suggest some sauce for your hat, it's Mezzetta's Habanero sauce with the appropriate words "Twist and Shout" on the label. It's definitely up there on the heat scale, but not as concentrated as the "Hell Hot" sauce which seems to have a lot of radioactive byproducts. Mezzetta's has a touch of sweet (?) taste along with the hot flavor, while others of just have the hot flavor piled on top of the hot flavor. Putting a teaspoon or two on the edge of your plate and adding a small bit to each bite can add that extra flavor to even the toughest dishes. ----- http://mindspring.com/~benbradley |
#34
|
|||
|
|||
Ben Bradley wrote: Bob, I expect you believe the shaker table description, so you shouldn't have to actually do it. Ben, you may not have seen it in my posts for the last week or so but I am no longer disputing that a Doppler distortion phenomeon exists and that your experiment would show it even with ideal speakers. It's patently obvious from the thought experiment of a speaker on a long swing emitting a tone. Where I remain in divergence from the mainstream is the cause of it. I do not believe that if you were to do the two tone experiment with a clean piston in a tube such that the boundry conditions enforce the creation of a plane wave, that you would see any Doppler distortion. Mainstream thinking says you would. The reason it doesn't is that the coupling of speaker to a distant receiver is a constant, frequency independant function in that case. I say that mixing does not occur at the piston/air interface but further out in the radiated field instead. What I am disputing at this point is the mechanism. It does not occur because of little fast waves riding on big slow ones in the cone but rather under circumstances where the coupling from speaker to detector is frequency dependant. A speaker in a box has a very frequency dependant coupling to the far field and will evidence Doppler distortion. An ESL in a push-pull configuration is a very low distortion emitter and has the advantage that the diapragm motion can be very accurately measured by incuding the capacitance between the diaphragm an one of the push-pull plates in a tuned RF modulator. An FM detector on that RF signal will quite accurately tell what the diaphragm is actually doing so as to provide a reference signal for any experiment. I predict that such a system will show no Doppler distortion in a tube if one can be constructed. The requisite terminations at the ends is probably too difficult, however. If it is too difficult, the ESL can be used free standing for a different experiment. If the principle of my theory of what causes Doppler distortion is correct, the amount of it will increase relative to the signal as you distance yourself from the speaker if the low frequency used in the experiment is low enough that its coupling to the receiver decreases much more rapidly with distance than the high frequency one. The principle I am trying to refute would make the amount of distortion relative to the signal independant of the receiver position in space. I can suggest some sauce for your hat, it's Mezzetta's Habanero sauce with the appropriate words "Twist and Shout" on the label. It's definitely up there on the heat scale, but not as concentrated as the "Hell Hot" sauce which seems to have a lot of radioactive byproducts. Mezzetta's has a touch of sweet (?) taste along with the hot flavor, while others of just have the hot flavor piled on top of the hot flavor. Putting a teaspoon or two on the edge of your plate and adding a small bit to each bite can add that extra flavor to even the toughest dishes. I will definitely save that recipe should either solid experiment or theory refute the principle on which I think an accurate theory can be based. :-) Without a full development of either, I've shown how the predictions of mine and the popular one will differ with a fairly easy experiment to set up and do (as experiments go.) Wish I could do it myself but I have neither the resources nor the available time. I still haven't seen any attempt at all to refute the argument which says it can't exist with a piston in a tube because of the principle of reciprocity. Several have hollered that reciprocity doesn't apply to pistons driving air but without a single detailed reason why not without appeal to sound pressures that yield a signifigantly non-linear relationship between pressure and velocity. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#35
|
|||
|
|||
"The Ghost" wrote in message om... THE HYPOTHESIS: Assuming that the equation for the Doppler frequency shift of a source moving at constant velocity also applies under dynamically changing velocity conditions, one would expect the propagating sound, that is produced by a high-frequency source moving dynamically at a low frequency around a fixed position, to be frequency modulated. One would further expect that the instantaneous frequency of the propagating sound would reflect the dynamic low-frequency velocity the source. If so, the waveform of the fm-demodulated high-frequency propagating sound, should follow on an instantaneous basis, the dynamic velocity of the low-frequency velocity of the source. THE SETUP: A small circular piezoelectric bimorph, having a resonant frequency of approximately 10KHz was attached to the 10-lb armature/shaft of a linear motor. The displacement of the armature/shaft was monitored by a linear displacement transducer attached to the opposite end of the armature/shaft. The linear displacement transducer also provided feedback for the servo amplifier which was driving the linear motor. Because the linear motor was in a servo loop, the displacement of the motor followed with reasonable accuracy both sinusoidal and non-sinusoidal command signals that were applied to the amplifier. The piezoelectric sound source was driven by a low-distortion oscillator at 10KHz. The sound emitted by the source was measured by a microphone at a distance of approximately one foot. The output of the microphone was amplified, high-pass filtered and applied to a frequency-to-voltage converter. The output of the frequency-to-voltage converter was low-pass filtered to reduce the level of the residual 10KHz carrier, amplified and applied to a signal averager. The signal averager was triggered by the command signal that was applied to the linear motor. Averaging was used in order to remove non-coherent 60Hz that was present in the output of the demodulator. THE MOTION OF THE SOUND SOURCE A triangular command signal having a 50-msec period was applied to the servo amplifier. A triangular command signal was used in order to simplify interpretation of the measurement result and to avoid the phase shift vs time delay ambiguity that would otherwise exist with fixed frequency sinusoidal excitation. The output of the displacement transducer was monitored on an oscilloscope and found to be triangular with rounded corners. The rounding of the corners is due to the limited closed-bandwidth of the servo. The velocity of the linear motor was therefore trapezoidal with relatively flat and relatively long plateaus and relatively short transitions. THE MEASUREMENT RESULT The propagating 10KHz signal emitted by the piezo bimorph was applied to an FFT analyzer in zoom-analysis mode with a resolution bandwidth of 0.1Hz. When the piezo bimorph was stationary, the propagating signal picked up by the microphone showed only a single spectral peak at 10KHz. When the piezo transducer was moving back and forth with a triangular displacement provided by the linear motor, the propagating signal received by the microphone contained numerous sidebands which were indicative of FM modulation. Additionally, the output of the FM demodulator was observed to be trapezoidal and followed on an instantaneous basis the velocity of the linear motor and the attached piezo transducer. THE CHALLENGE In science, theory usually follows experimental results. In this case the experimental result shows that a 10KHz signal applied to a small piezoelectric source moving back and forth around a fixed position becomes frequency modulated by the back and forth motion of the source. The measurement further shows that the received, FM-demodulated signal follows the instantaneous velocity of the source. This result is exactly what is expected on the basis of Doppler frequency shift extrapolated from constant velocity to dynamic velocity conditions. While some might argue that the observed FM-like sidebands and the trapezoidal demodulated waveform are the result of IM distortion, and not Doppler FM, the ball is in their court. It is now up to them to provide an explanation/analysis involving an IM producing mechanism in the present experimental setup that accounts for the present experimental result. Finally, it must be noted that the purpose of the present measurement was to demonstrate fundamental phenomenological behavior. The 10KHz carrier and the 50-msec peridiocity for the displacement of the linear motor were chosen solely to accommodate the hardware on hand. There is presently no reason to believe that the outcome of the present measurement would be different if other carrier frequencies or other source displacement periodicities or waveshapes were used. I agree with everything you've said, except that it doesn't apply to loudspeakers, you've just come up with a fancier variation of the train/whistle model, which doesn't apply to speakers because the speaker is reproducing a complex soundwave in toto from a single complex driving source, what you're doing is the same as picking up the speaker and moving it back and forth and that will certainly produce Doppler shift. It isn't that the motion is dynamic, it's that the motion is coming from a single source which producing a complex sound, that is the reason a speaker doesn't produce doppler shift when reproducing music. |
#36
|
|||
|
|||
He was correct and you are not. It is entirely a matter of the frequency dependant coupling. Bob, If you set up your coupling tube so that the speaker cone pushes the air completly and the air moves in the tube without loss and at the far end the air pushes the mic diaphram completly SO THAT THE SPEKAER CONE AND MIC DIPHRAM ARE MOVING TOGETHER IN LOCK STEP WITH THE SAME DISPLACEMENT, then you are correct, there is no Doppler effect. Note that in this case the distance between the Rx and Tx is constant and there is no Doppler effect. In any other case where the mic diaphram is not moving in lock step with the cone, there will be a Doppler effect. Mark |
#37
|
|||
|
|||
Sorry to come in so late on this thread, but wasn't this topic the subject
of Dr. Klipsch's research and the basis of the K-horn design? Mike Squires -- Mike Squires (mikes at cs.indiana.edu) 317 233 9456 (w) 812 333 6564 (h) mikes at siralan.org 546 N Park Ridge Rd., Bloomington, IN 47408 |
#38
|
|||
|
|||
Bob Cain wrote in message ...
The Ghost wrote: ......... The absence of a quantitative description of a phenomenon is not a justifiable excuse for denying its existence. In the history of science, there are many phenomena that were demonstrated first and quantified later. Evidence for existence of a phenomenon requires elimination of spurious causes one way or another, either by experimental setup or by having a _good_ characterization of the spurious phenomena so that their effect can be removed from the test data. How does your "experiment" do either so that what remains can be legitimately regarded as evidence of Doppler distortion? I contend that my experiment has no so-called spurious phenomena. Since you are the one claiming that it does, it is your responsibility to identify them and demonstrate, with your own measurements, that my measurement results are invalidated when the so-called spurious phenomena are removed. Given that my measurement result agree with expectation that the instantaneous FM-demodulated propagating signal follows in time the instantaneous trapezoidal velocity of the source, I seen no need to go looking for so-called spurious phenomena which exist only in your mind. And even if it satisfied that requirement, the phenomenon in question now is not simply Doppler distortion but the mechanism that produces it so a predictive model is absolutely required. Why, if the mechanism is as simple as is described, has no such model been forthcoming? The mechanism for instantaneous Doppler shift is instantaneous relative motion between the source and the observer. Beyond that, any predictive model would necessarily have to be situation specific, and in that regard, the simplest situations to model are the most difficult to experimentally verify and vice versa. This is basic stuff and should not have to be spoon fed to anyone who claims to be an experimental scientist. It is you, not I, who is having problems understianding this basic stuff. |
#39
|
|||
|
|||
Mark wrote: If you set up your coupling tube so that the speaker cone pushes the air completly and the air moves in the tube without loss and at the far end the air pushes the mic diaphram completly SO THAT THE SPEKAER CONE AND MIC DIPHRAM ARE MOVING TOGETHER IN LOCK STEP WITH THE SAME DISPLACEMENT, then you are correct, there is no Doppler effect. Yes, exactly. And if they aren't I'd like to be shown why, exactly and without any unparamaterized or underived formulas. All axioms should be stated for purposes of criticism and a derivation proceed from there to a proof that reciprocity fails in this case. Because if it doesn't, then if you make the active piston passive and measure motion due to passage of a wave (coming from the side of it opposite the receiver) and then make the piston active to generate the same motion, the reciever at the end will see two different things. I don't believe it. I really don't expect any of my opponents in this debate to address this because it seems they never do if they can't explain it and then it remains invalid by their silence as if it had never been uttered. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#40
|
|||
|
|||
|
Reply |
Thread Tools | |
Display Modes | |
|
|
Similar Threads | ||||
Thread | Forum | |||
Audiophile glossary | High End Audio | |||
science vs. pseudo-science | High End Audio | |||
Why DBTs in audio do not deliver (was: Finally ... The Furutech CD-do-something) | High End Audio | |||
Negative/Positive Phase Shift in a Transformer | Pro Audio |