On Sun, 8 Aug 2004 19:14:50 +0200, "Wessel Dirksen"
wrote:
"Goofball_star_dot_etal" wrote in message
...
On Fri, 06 Aug 2004 06:49:53 +0100, Don Pearce
wrote:
On Thu, 5 Aug 2004 22:19:23 -0400, "Arny Krueger"
wrote:
Here's the results of some speaker measurements that I made tonight,
based
on passing 50 Hz & 4 KHz mixed 1:1 at about 1.2 volts rms, through a
Peerless 6.5 inch woofer with about 6 mm Xmax (relatively large for a
woofer
its size). The speaker is mounted in a roughly 0.4 cubic foot box with
no
vent. The power amp is a QSC USA 850. This is not very loud. The mic is
an
ECM8000 that is a few inches from the woofer cone.
http://www.pcavtech.com/techtalk/doppler/
The first graph shows the broadband response. The large spikes at 50 Hz
and
4 KHz are clearly visible. The second and third harmonics of the 50 Hz
tone
are about 30 dB down. The spike for the 4 KHz tone is about 5 dB higher
than
the spike for 50 Hz because the woofer is simply that much more
efficient at
4 KHz.
The second graph is taken from the same test, with the frequency scale
enlarged to show about 400 Hz on either side of 4 KHz. The first pair
of
large spikes are about 50 Hz on either side of 4 KHz, the second are
about
100 Hz on either side of 4 KHz, and so on. The distortion products are
probably a mixture of AM and FM distortion, with FM predominating, as
the
test is contrived to focus on FM.
While I've got this set up, any other data that anyone would find
interesting?
Well, speakers generally are nonlinear, so what you are seeing here is
intermod. Doppler distortion in speakers is supposedly a "built-in"
effect - nothing to do with non-liearity - that is caused by the same
cone reproducing two frequencies simultaneously. The argument goes
that if a speaker is reproducing a 1kHz tone, but is simultaneously
moving back and forth at 50Hz, the 1kHz tone must be modulated by the
Doppler effect. Of course, if you do the maths of superposition, this
doesn't happen - the tones coexist perfectly without any doppler.
I don't think anyone intended that "superposition" be used
willie-nilly. How about an explanation of why a moving "tweeter"
does not produce doppler.
IM effects, of which doppler summation are a part IMO, are also dependant on
total piston excursion. Thus large diameter woofers suffer less from such
effect at low frequencies. Since cone excursion is reduced inversely with
increasing frequency, IM effects become progressively more negligable.
Arny's 2 different frequency suites seem to show this. Also a two tone test
suite is never free of FM affects because a complete higher frequency cycle
will always originate at different excursion locations within the excursion
pattern governed by the low frequency leading to the lower frequency
modulated phase shifting. Ideally one would want to use a non-harmonic or
randomized stimulus at a low frequency/high excursion and then measure the
effect on the higher signal.
Well, this is all very interesting but it does not address whether The
Pinciple of Linear Superposition is applicable to this case.
Don Pearce claims, in effect, to have THE LAWS OF PHYSICS and MATHS on
his side. However, he argues that (he wishes) there is no FM
therefore superposition proves that he is correct in his original wish
that the system is linear, so that superposition applies, and
therefore no FM occurs.
Wessel
I note that you did not take the hint (in the thread "Speaker
transient analysis") that I thought your statement:
"So yes,the acoustical output is directly proportional to the velocity
(not the force applied)" was incorrect.
Svante wrote:
p=U*rho0*w/(4*pi*r)
where U is the volume flow in m3/s (=surface*velocity), rho0=1.2kg/m3,
w is the angular frequency, and r is the distance.
After some thinking about this equation, one can realise that sound
pressure is roportional to the piston *acceleration* (comes from w*U,
ie derivative of the flow).
Nobody else seemed to notice that these two statements were different.
.. .
So this is simple, stright-forward intermodulation between the two
tones.
d
Pearce Consulting
http://www.pearce.uk.com