Sum of Two Acoustic Sources

If I have two acoustic sources transmitting the exact same signal
(perfectly correlated), i.e., a stereo system playing a monaural
signal, then what total power would be perceived at the listening
position without accounting for path loss? Let's say each channel
(left and right) is transmitting the exact same acoustic power, P
watts. Let's also assume we're in an anechoic chamber so that there
are no reflections, and that the positioning and symmetry is perfect.

On the one hand, you'd expect 2P watts at the listening position,
i.e., a 3 dB increase. That makes sense - two speakers, 3 dB
increase in power.

But on the other hand, you might expect acoustic pressures to sum, so
that you'd get a 6 dB increase. But this doesn't seem to make sense
since you'd be getting 3 dB better than the available power.

Does near-field/far-field matter?

Any help educating me would be appreciated. I have the Beranak and
Zwicker texts but obviously and not too familiar with them, but
they are available for reference should you care to point me to
the right page.
--
% Randy Yates % "And all that I can do
%% Fuquay-Varina, NC % is say I'm sorry,
%%% 919-577-9882 % that's the way it goes..."
%%%% % Getting To The Point', *Balance of Power*, ELO
http://home.earthlink.net/~yatescr

"Randy Yates" wrote in message
...
If I have two acoustic sources transmitting the exact same signal
(perfectly correlated), i.e., a stereo system playing a monaural
signal, then what total power would be perceived at the listening
position without accounting for path loss? Let's say each channel
(left and right) is transmitting the exact same acoustic power, P
watts. Let's also assume we're in an anechoic chamber so that there
are no reflections, and that the positioning and symmetry is perfect.

On the one hand, you'd expect 2P watts at the listening position,
i.e., a 3 dB increase. That makes sense - two speakers, 3 dB
increase in power.

But on the other hand, you might expect acoustic pressures to sum, so
that you'd get a 6 dB increase. But this doesn't seem to make sense
since you'd be getting 3 dB better than the available power.

Does near-field/far-field matter?

Any help educating me would be appreciated. I have the Beranak and
Zwicker texts but obviously and not too familiar with them, but
they are available for reference should you care to point me to
the right page.
--
% Randy Yates % "And all that I can do
%% Fuquay-Varina, NC % is say I'm sorry,
%%% 919-577-9882 % that's the way it goes..."
%%%% % Getting To The Point', *Balance of
Power*, ELO
http://home.earthlink.net/~yatescr

I'll vote for getting a maximum of twice the power. You will have to ignore
the possibility that there will be some interference between the two, in
which case you could get zero power in some places.

Michael

Randy Yates wrote:
If I have two acoustic sources transmitting the exact same signal
(perfectly correlated), i.e., a stereo system playing a monaural
signal, then what total power would be perceived at the listening
position without accounting for path loss? Let's say each channel
(left and right) is transmitting the exact same acoustic power, P
watts. Let's also assume we're in an anechoic chamber so that there
are no reflections, and that the positioning and symmetry is perfect.

On the one hand, you'd expect 2P watts at the listening position,
i.e., a 3 dB increase. That makes sense - two speakers, 3 dB
increase in power.

But on the other hand, you might expect acoustic pressures to sum, so
that you'd get a 6 dB increase. But this doesn't seem to make sense
since you'd be getting 3 dB better than the available power.

Does near-field/far-field matter?

Google "ripple tank"
http://demo.physics.uiuc.edu/LectDem....idc?DemoID=48
http://www.physics.montana.edu/demon...aterwaves.html
http://en.wikipedia.org/wiki/Ripple_tank

Two waves will either add or subtract intensity, depending on their
relative *phase*, which will vary with their distance from their
sources (and the relative phase at the moment they are emitted).

The pattern produced is one of 'beams' of waves spreading out as they
get further from the source. 'On' the beam the intensity adds up, but
between the beams the intensity subtracts and a 'dead space' is
produced.

The exact geometry of these 'beams' will depend on the wavelength of
the wave and the distance between the sources as well as the speed of
the waves.

In ripple tank images, the 'beams' are zones where the wave pattern is
clear and strongest, and the 'dead zones' are the areas where the
ripple pattern is fuzziest and grey.

As the images in the Wiki article suggest, the presence of reflective
barriers complicates the acoustics immensely as each point on the wall
can be treated as another 'source'.

HTH

Tom Davidson
Richmond, VA