On 1 Dec 2003 11:57:39 -0800, (Bob-Stanton)
wrote:


To say: "You cannot sum individual powers", is a violation of the law
of conservation of energy.


A serious charge. . .


Another fundamental law a physics is Energy = Force * Distance. If
each of four drivers in an array is pushing the air with half the
force, for half the distance, each puts out 1/4 the energy. The total
power output of four will be only the same as a single driver.

You are not pushing air with half the force you are pushing the
mass/stiffnes/damping of the driver with half the force. On the output
side of the driver the work is volume * pressure. Each driver sees its
own pressure plus the pressure of three more drivers. Each driver does
four times the work on the air that it would do if it saw only its
own pressure. This is not a "violation of the law of conservation of
energy" since it bears little relationship to the electrical input
power which only increases very slightly due the negligible increase
in load.

(Bob-Stanton) wrote in message . com...
(Svante) wrote in message


You cannot sum the powers. You have to sum the sound pressures. The
sum of four 1/2 pressures is 2. So, sound pressure will double (+6.02
dB) for the same input power.
...

No, again you cannot sum the individual powers.

To say: "You cannot sum individual powers", is a violation of the law
of conservation of energy.

Assuming that there is no change in the acoustic power from each
speaker... You are going in circles, you say that efficiency does not
change, because efficiency does not change.

Another fundamental law a physics is Energy = Force * Distance. If
each of four drivers in an array is pushing the air with half the
force, for half the distance, each puts out 1/4 the energy. The total
power output of four will be only the same as a single driver.

The distance is halved, but the force is not. Each driver sees the
pressure created by itself, but also the pressure from three more
drivers. Thus the pressure is four times half the original pressure (=
two times the original pressure), and thus the force is doubled. So if
energy = force * distance, and the force is doubled, the distance is
halved, and the number of drivers is four, the net energy will be four
times the single driver.

For the system, total
displacement will be x*2. This is acheived with the the same input
power. This corresponds to an increased efficiency of +6.02 dB.


Thats right. BUT
the force exerted by the drivers in the array is only 1/2 that of a
single driver, that corresponds to a decreased efficiency: -6.02 dB.

Nope, see above.


6.02 dB -6.02 dB = 0 dB change.

P = F/2 * x*2 is the same pressure as: F * x. That means NO increase
in pressure, No incease in effiency and no increase in power.


This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)


No. Given an ideal piston driven to an acceleration corresponding to
the signal, the level EXACTLY straight in front of and far away from
the piston does NOT vary with frequency. To the sides it does. To the
sides the level will vary towards higher frequencies due to
interference from the different parts of the piston. This will cause
on-axis level to be constant (vs frequency), but efficiency to drop
towards higher frequencies. Thus, the efficiency gain I have described
in this thread is only acheived in the low-frequency region.

At higher frequencies, as the polar pattern narrows, the energy will
be concentrated toward the front. The sound pressure level will
increase.

Bob Stanton

(Bob-Stanton) wrote in message . com...
(Svante) wrote in message


You cannot sum the powers. You have to sum the sound pressures. The
sum of four 1/2 pressures is 2. So, sound pressure will double (+6.02
dB) for the same input power.
...

No, again you cannot sum the individual powers.

To say: "You cannot sum individual powers", is a violation of the law
of conservation of energy.

Assuming that there is no change in the acoustic power from each
speaker... You are going in circles, you say that efficiency does not
change, because efficiency does not change.

Another fundamental law a physics is Energy = Force * Distance. If
each of four drivers in an array is pushing the air with half the
force, for half the distance, each puts out 1/4 the energy. The total
power output of four will be only the same as a single driver.

The distance is halved, but the force is not. Each driver sees the
pressure created by itself, but also the pressure from three more
drivers. Thus the pressure is four times half the original pressure (=
two times the original pressure), and thus the force is doubled. So if
energy = force * distance, and the force is doubled, the distance is
halved, and the number of drivers is four, the net energy will be four
times the single driver.

For the system, total
displacement will be x*2. This is acheived with the the same input
power. This corresponds to an increased efficiency of +6.02 dB.


Thats right. BUT
the force exerted by the drivers in the array is only 1/2 that of a
single driver, that corresponds to a decreased efficiency: -6.02 dB.

Nope, see above.


6.02 dB -6.02 dB = 0 dB change.

P = F/2 * x*2 is the same pressure as: F * x. That means NO increase
in pressure, No incease in effiency and no increase in power.


This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)


No. Given an ideal piston driven to an acceleration corresponding to
the signal, the level EXACTLY straight in front of and far away from
the piston does NOT vary with frequency. To the sides it does. To the
sides the level will vary towards higher frequencies due to
interference from the different parts of the piston. This will cause
on-axis level to be constant (vs frequency), but efficiency to drop
towards higher frequencies. Thus, the efficiency gain I have described
in this thread is only acheived in the low-frequency region.

At higher frequencies, as the polar pattern narrows, the energy will
be concentrated toward the front. The sound pressure level will
increase.

Bob Stanton

(Svante) wrote in message


Nope, see above.


I set up a test. I had an array of four drivers. I wired them such
that I could switch from a single driver to an array of four.

I measure the sound power levels at:
60 Hz
70 Hz
80 Hz
90 Hz
100 Hz
120 Hz
140 Hz

Switching from a single driver to an array of four, I measured an
increase in sound power level of 5.5 to 6.5 dB. Even varying the
distance of the sound power level meter from 3 ft to 6 ft, I still got
a consistant +6 dB change, just as you perdicted.

Bob Stanton

(Svante) wrote in message


Nope, see above.


I set up a test. I had an array of four drivers. I wired them such
that I could switch from a single driver to an array of four.

I measure the sound power levels at:
60 Hz
70 Hz
80 Hz
90 Hz
100 Hz
120 Hz
140 Hz

Switching from a single driver to an array of four, I measured an
increase in sound power level of 5.5 to 6.5 dB. Even varying the
distance of the sound power level meter from 3 ft to 6 ft, I still got
a consistant +6 dB change, just as you perdicted.

Bob Stanton

(Svante) wrote in message


Nope, see above.


I set up a test. I had an array of four drivers. I wired them such
that I could switch from a single driver to an array of four.

I measure the sound power levels at:
60 Hz
70 Hz
80 Hz
90 Hz
100 Hz
120 Hz
140 Hz

Switching from a single driver to an array of four, I measured an
increase in sound power level of 5.5 to 6.5 dB. Even varying the
distance of the sound power level meter from 3 ft to 6 ft, I still got
a consistant +6 dB change, just as you perdicted.

Bob Stanton

(Bob-Stanton) wrote in message . com...
(Svante) wrote in message


Nope, see above.


I set up a test. I had an array of four drivers. I wired them such
that I could switch from a single driver to an array of four.

I measure the sound power levels at:
60 Hz
70 Hz
80 Hz
90 Hz
100 Hz
120 Hz
140 Hz

Switching from a single driver to an array of four, I measured an
increase in sound power level of 5.5 to 6.5 dB. Even varying the
distance of the sound power level meter from 3 ft to 6 ft, I still got
a consistant +6 dB change, just as you perdicted.

Bob Stanton

Great! This proves that the best way to settle things when one runs
out of theoretical arguments is to examine the real world. Which you
did, and I should have. My compliments.

Just a small question here, were you outdoors or indoors? Big
room/small room? Was the level increase consistent in different
directions?

(Bob-Stanton) wrote in message . com...
(Svante) wrote in message


Nope, see above.


I set up a test. I had an array of four drivers. I wired them such
that I could switch from a single driver to an array of four.

I measure the sound power levels at:
60 Hz
70 Hz
80 Hz
90 Hz
100 Hz
120 Hz
140 Hz

Switching from a single driver to an array of four, I measured an
increase in sound power level of 5.5 to 6.5 dB. Even varying the
distance of the sound power level meter from 3 ft to 6 ft, I still got
a consistant +6 dB change, just as you perdicted.

Bob Stanton

Great! This proves that the best way to settle things when one runs
out of theoretical arguments is to examine the real world. Which you
did, and I should have. My compliments.

Just a small question here, were you outdoors or indoors? Big
room/small room? Was the level increase consistent in different
directions?

(Bob-Stanton) wrote in message . com...
(Svante) wrote in message


Nope, see above.


I set up a test. I had an array of four drivers. I wired them such
that I could switch from a single driver to an array of four.

I measure the sound power levels at:
60 Hz
70 Hz
80 Hz
90 Hz
100 Hz
120 Hz
140 Hz

Switching from a single driver to an array of four, I measured an
increase in sound power level of 5.5 to 6.5 dB. Even varying the
distance of the sound power level meter from 3 ft to 6 ft, I still got
a consistant +6 dB change, just as you perdicted.

Bob Stanton

Great! This proves that the best way to settle things when one runs
out of theoretical arguments is to examine the real world. Which you
did, and I should have. My compliments.

Just a small question here, were you outdoors or indoors? Big
room/small room? Was the level increase consistent in different
directions?

(Svante) wrote in message

Great! This proves that the best way to settle things when one runs
out of theoretical arguments is to examine the real world. Which you
did, and I should have. My compliments.

Just a small question here, were you outdoors or indoors? Big
room/small room? Was the level increase consistent in different
directions?



The room was part of an attic, 16 ft by 24 ft, with sloping walls.

The drivers in the array were 4 in "woofers". They were mounted only 8
inches on center. When I switched to a single driver, the acoustical
center changed by only 5 in.

The power measured, I'm sure, was incident wave + room standing wave.
Since the source location changed by only 5 in, the ratio of incident
to standing wave didn't change too much, keeping the measurements
fairly accurate.

It was fun, and I learned a lot.

Regards,

Bob Stanton

(Svante) wrote in message

Great! This proves that the best way to settle things when one runs
out of theoretical arguments is to examine the real world. Which you
did, and I should have. My compliments.

Just a small question here, were you outdoors or indoors? Big
room/small room? Was the level increase consistent in different
directions?



The room was part of an attic, 16 ft by 24 ft, with sloping walls.

The drivers in the array were 4 in "woofers". They were mounted only 8
inches on center. When I switched to a single driver, the acoustical
center changed by only 5 in.

The power measured, I'm sure, was incident wave + room standing wave.
Since the source location changed by only 5 in, the ratio of incident
to standing wave didn't change too much, keeping the measurements
fairly accurate.

It was fun, and I learned a lot.

Regards,

Bob Stanton

(Svante) wrote in message

Great! This proves that the best way to settle things when one runs
out of theoretical arguments is to examine the real world. Which you
did, and I should have. My compliments.

Just a small question here, were you outdoors or indoors? Big
room/small room? Was the level increase consistent in different
directions?



The room was part of an attic, 16 ft by 24 ft, with sloping walls.

The drivers in the array were 4 in "woofers". They were mounted only 8
inches on center. When I switched to a single driver, the acoustical
center changed by only 5 in.

The power measured, I'm sure, was incident wave + room standing wave.
Since the source location changed by only 5 in, the ratio of incident
to standing wave didn't change too much, keeping the measurements
fairly accurate.

It was fun, and I learned a lot.

Regards,

Bob Stanton

Bob-Stanton wrote:
... Switching from a single driver to an array of four, I measured an
increase in sound power level of 5.5 to 6.5 dB. Even varying the
distance of the sound power level meter from 3 ft to 6 ft, I still got
a consistant +6 dB change, just as you predicted.

Bob Stanton

Thanks, Bob.
I was just getting ready to buy a dartboard.

That makes sense. I put a matching pair of speaker cabinets,
each with a four-speaker cluster, on a stereo amp, mono in,
outputs matched. These were the Audax PR-17 mids, with the
signal filtered to 300-8K through a TDM stereo 24 dB/octave
electronic crossover. I ran noise from a Gold-Line pink
noise generator. A picture of these cabinets is in a previous
post.

When I disconected three of the drivers from one side, the
the quad array was definitely much louder. I didn't measure
the actual output but there was a marked difference.

And thank you all for your responses.

________________ Marc Stager

Bob-Stanton wrote:
... Switching from a single driver to an array of four, I measured an
increase in sound power level of 5.5 to 6.5 dB. Even varying the
distance of the sound power level meter from 3 ft to 6 ft, I still got
a consistant +6 dB change, just as you predicted.

Bob Stanton

Thanks, Bob.
I was just getting ready to buy a dartboard.

That makes sense. I put a matching pair of speaker cabinets,
each with a four-speaker cluster, on a stereo amp, mono in,
outputs matched. These were the Audax PR-17 mids, with the
signal filtered to 300-8K through a TDM stereo 24 dB/octave
electronic crossover. I ran noise from a Gold-Line pink
noise generator. A picture of these cabinets is in a previous
post.

When I disconected three of the drivers from one side, the
the quad array was definitely much louder. I didn't measure
the actual output but there was a marked difference.

And thank you all for your responses.

________________ Marc Stager

Bob-Stanton wrote:
... Switching from a single driver to an array of four, I measured an
increase in sound power level of 5.5 to 6.5 dB. Even varying the
distance of the sound power level meter from 3 ft to 6 ft, I still got
a consistant +6 dB change, just as you predicted.

Bob Stanton

Thanks, Bob.
I was just getting ready to buy a dartboard.

That makes sense. I put a matching pair of speaker cabinets,
each with a four-speaker cluster, on a stereo amp, mono in,
outputs matched. These were the Audax PR-17 mids, with the
signal filtered to 300-8K through a TDM stereo 24 dB/octave
electronic crossover. I ran noise from a Gold-Line pink
noise generator. A picture of these cabinets is in a previous
post.

When I disconected three of the drivers from one side, the
the quad array was definitely much louder. I didn't measure
the actual output but there was a marked difference.

And thank you all for your responses.

________________ Marc Stager