Re: Re: Why would more sound travel through two materials than one alone?

There are a lot of variables involved with speaker efficiency, so what you
experienced may not always be the case.  If I had more specifics on your
experiment, I could probably provide a better answer, but I will give the
best explanation I can, though I will have to be rather broad.  Some things
that would have been helpful in providing an explanation would be 

A.  The type of speaker (make and model)
B.  The size of the speaker
C.  The dimensions of the box.
D.  The audio source (constant frequency?  Music?  Speech?  Very important)
E.  Power source (in RMS and peak wattage, just for an idea of how close
the speaker was being pushed to its limit)
F.  A spectrograph analysis of each case (to show which frequency bands
increased in amplitude and which were decreased)

It is possible that changes in any of these variables would have altered
your outcome, as will become apparent as I continue.  

Also, you say that the speaker was sealed in the box, but an exact idea of
HOW sealed would also be helpful.  For instance, you did have to run wires
into the box, so whether that was done through a set of connectors which
were mounted on one wall of the box or whether that was done by running
wires through a hole in the box also makes a difference...

Also, was the styrofoam lining mounted very solidly with glue, or was it
just kind of placed inside?  The results would probably be different
between those cases as well.

Now, down to the explanation...

There are three primary possibilities I see in this case.  The first
possibility I see is that the styrofoam was acting as a passive radiator. 
The second is that perhaps you had a hole in the box to run wires through
or for some other reason, and the hole was causing the enclosure to act as
a Helmholtz resonator.  The third is that the conditions inside the box
with the styrofoam inside JUST HAPPENED, by chance, to be closer to the
conditions that the speaker was designed for (specifically concerning
changing pressure conditions).

Passive radiation is used in speaker enclosures to increase audio output
within a certain frequency range primarily by picking a radiator with
specific resonance characteristics.  The box is sealed, and, in most cases,
the passive radiator is a speaker cone similar to the active speaker, but
it is not powered by a magnet or electricity in any form or fashion.  The
movement of the passive radiator is caused by the sound waves produced by
the active speaker and the changing pressure within the enclosure.  As the
frequency produced by the active speaker nears the resonance of the passive
radiator, the passive radiator will begin to resonate and will produce a
second sound wave.  If the enclosure is properly designed, the two sound
waves will be constructive (that is, the peaks of the two waves will
coincide, and the troughs of the two waves will coincide so as to produce a
total wave which is larger than either of the two original waves).  If the
enclosure is poorly constructed, the sound wave created by the passive
radiator could have a 180 degree phase relation with the primary wave
created by the active speaker, and the combination of the two waves will be
destructive (that is, the peak from wave 1 coincides with a trough from
wave 2, and a peak from wave 2 coincides with a trough from wave 1, so when
you add the two waves together, the result is a wave which has a lower
amplitude than either of the two original waves).  

That being said, it is possible that the addition of the styrofoam lining
the box caused each surface of the box to resonate at frequencies which the
speaker was putting out.  Thus, the whole box was acting as a passive
radiator, or each face of the box was acting as a passive radiator, and
rather than absorbing the sound wave, each face was reradiating that sound
wave.  Note that this is NOT amplification as you put it, but rather, an
increase in efficiency.  You cannot create energy, but, you can make things
more efficient by keeping the energy from being turned into another kind of 
energy.  With the original plywood box, the box could have been absorbing
the sound energy and turning it into thermal energy (heat), while the
addition of the styrofoam changed the characteristics of the box so that
rather than convert the sound energy into heat, it took the sound energy
and reradiated it as another wave of sound energy.

OK, so there you have the explanation for the first possibility.

The second possibility I see is that maybe there was a hole in the box for
the wires or there was an opening in the box because of a mistake in its
construction.  This could cause the box to act as a Helmholtz resonator
(or, should I say, the air within acts as the resonator).  The example I
see for Helmholtz resonation the most is "It's like when you blow across
the top of a bottle."  Essentially, a ported speaker enclosure (one with a
hole in it) is tuned so that as the air moves in and out of the box through
the hole, the changing pressure caused by the air moving in and out sets up
a resonant oscillation.  The "in and out" movement of air causes a sound wave.

"Well, hold on," you might be saying.  "The hole did not change in size
when the box was lined with styrofoam!"  True, but the styrofoam did
decrease the volume of the box, and it is also possible that the styrofoam
sealed other holes that air may have been escaping from.  It is possible
that the addition of styrofoam caused the box to be tuned to a frequency
which was moreprevalently produced by your speaker.  If so, then the box
would only begin to act as a Helmholtz resonator in the case with the
styrofoam, or perhaps it acts as a Helmholtz resonator in both cases, but
it was tuned to a better frequency in the second case.

Almost done here...

The third case that could have taken place is that the enclosure just
happened by chance to be closer to the manufacturer's intentions for the
speaker when you lined it with styrofoam.  Most speakers are designed to be
mounted in the front of a box, where there is a counteracting pressure
inside the box to oppose the speaker's movement.  As the speaker cone moves
inward, the pressure inside the box increases due to the compression of the
air inside, and since the pressure on the inside surface of the cone is
higher than the pressure on the outside surface of the cone, the net force
on the cone caused by the air pressure is outward.  The roles are reversed
as the cone is forced outward by the electromagnetic field produced by the
speaker's voice coil...as the cone is forced out by the voice coil, there
is a counteracting force caused by the difference in air pressures inside
and outside, and the air pressure forces the cone inward as the voice coil
forces the cone outward.

Now, I'm not even sure whether the speaker you had inside this box was in
its own smaller enclosure or not, but assuming that it was not in a second
smaller enclosure, you essentially had it in a "free-air" situation where
there were no opposing forces caused by air pressure.  The speaker probably
was not designed for that, and it may not have been operating correctly
because of this.  

When the styrofoam was put inside, you may have reduced the volume of the
box enough to make it less like the open environment, or perhaps the
proximity of the speaker's cone face to a wall of styrofoam allowed for an
increased pressure on the face of the cone, allowing for less of a free-air
environment.  Normally, the free-air situation will be more efficient, but
if you were playing music which was complex, perhaps the speaker was not
operating well at all in this free-air situation.

If I had to guess as to which of these situations is most likely to be the
root cause, I'd have to go with scenario one, followed by two, then three.
 Resonance of the enclosure is most likely the cause.

If you decide to revisit this experiment, you can draw better conclusions
by having very specific and accurate data.  I would suggest using a very
controlled power source, and also a very controlled audio source.  Do not
use music as your source, as the speaker may not even be able to accurately 
reproduce multiple frequencies at once.  Rather, use a wave generator as
the audio source which will allow you to control the frequencies very
precisely.  You can do a sweep from 20 hz to 20 khz (provided you have
speakers which can produce these frequencies) and record the audio output
not just in decibels, but rather in a spectrograph-like form.  If you are
feeding the speaker a 500hz frequency, but the output which you are getting
shows a peak at 500hz AND another wave at 250hz, you may be getting
harmonic resonance, and that would be important to note.  

It would also be important to have a third "control" situation where the
speaker is not inside a box at all.  That way, you can compare all other
results to the control result, rather than comparing experimental results
to each other.  Perhaps you did this and did not mention it, but if you
decide to redo this experiment, this is pretty important.  You need a
control situation that is as untampered with as possible.

Also, it would be a good idea to use a microphone that has very flat,
accurate, and wide frequency response.  Cheap microphones pick up better in
the midrange frequencies, and may not pick up below 100hz or above 12khz at
all.  The best results will be obtained using studio condenser microphones 
which have extremely flat and accurate frequency response across the whole
hearing spectrum.  If you used a cheap microphone, you may have been
missing out on something important.

It would also be good to be in a room which has sound absorbing foam on the
walls and ceiling and has a carpeted floor, but I doubt you have access to
such a room.  I certainly do not.  But you would get poor results if you
chose something like a gym or a room with tile floor and painted concrete
walls.  The reverberation within the room would skew your results for sure.

Here are some links which I think will be helpful.  

Helmholtz resonance: http://www.phys.unsw.edu.au/jw/Helmholtz.html

Wave addition: http://www.udel.edu/idsardi/sinewave/sinewave.html
(try setting the two waves to be exactly the same, but only change the
phase relation.  This would be relevant to the discussion)

Speaker enclosures: http://electronics.howstuffworks.com/speaker9.htm
(sorry, its the most reliable source I have on enclosures, but from what I
see, the information is accurate)

If I come across any more relevant information, I will come back and post more.

I hope this helps your total understanding of the subject!

sincerely,

Joel