Physics of sound waves (reflection vs transmission) question

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Ker_01 - 30 Jun 2008 17:37 GMT

I'm not a physicist, so I'm hoping someone can answer or point me to
information that explains the following in layman's terms.

I understand that sound can be absorbed, reflected, or transmitted (again,
layman's terms). When building a sound-proof wall, the construction advice
is to set up two separate stud walls (one for either side) so that sound
isn't tranmitted from the drywall on one side, through the wood studs,
directly to the drywall on the other side. My general impression is that it
is because the change in material density from drywall-wood-air
cavity-wood-drywall has more changes in density and perhaps the change to
airborne (and back) is a density change of higher magnitude, with the idea
that sound hitting a denser barrier will cause more of the sound to be
reflected (rather than transmitted).

What specific aspects of a substrate affect sound transmission versus
reflection? For example, if I want a permanent soundproof wall to minimize
transfer of loud neighbor or child's instrument practice, should I focus on
density change, number of transitions... or something else?

What are the limitations (based on the physics of soundwaves), such as the
distance between density changes (e.g. layers of mylar separated by 1mm of
air vs being separated by wider distances) vs the length of a soundwave?

What is the effect of actual change in substrate density (dense-to-dense
substrate vs dense-to-air) vs the wavelength or amplitude of the soundwave?

I also recognize that foam, blankets, and other softer substrates can absorb
sound, but (other than layering them inside the wall) I'm trying to end up
with clean interior design and would avoid them if possible.

Best regards,
Keith

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Androcles - 30 Jun 2008 19:21 GMT

| I'm not a physicist, so I'm hoping someone can answer or point me to
| information that explains the following in layman's terms.
[quoted text clipped - 14 lines]
| transfer of loud neighbor or child's instrument practice, should I focus on
| density change, number of transitions... or something else?

The first thing to note is that you are using conventional building
materials
which will limit the range of choice. Theoretically you could use a metallic
wall such as lead, for example, which has often been used as roofing
material since medieval times and is still in use today.
http://www.k-roofing.co.uk/images/slate_roof_lead_valley_4.jpg

In apartment blocks the nuisance direction is more usually vertical and
a concrete floor can be greatly improved with a thick carpet.

The second thing to note is frequency. Low frequencies tend to propagate
further than high frequencies - thunder - fog horns - boom boxes - if the
neighbourhood kid's musical instrument is a picolo it will disturb you far
less than if it is a set of drums. Most pop music has a repetitive low
frequency beat with some simple melody laid over it and all too often
the beat can be heard without the melody when masked by some barrier.

| What are the limitations (based on the physics of soundwaves), such as the
| distance between density changes (e.g. layers of mylar separated by 1mm of
| air vs being separated by wider distances) vs the length of a soundwave?

Low A on a piano is 27.5 Hz,
http://en.wikipedia.org/wiki/Piano_key_frequencies
and the speed of sound is 343 m/s .
This gives lambda = 343/27.5 = 12.5 meters = about 40 feet.
Unless you live in a huge stone castle, wall thickness is not an option.

| What is the effect of actual change in substrate density (dense-to-dense
| substrate vs dense-to-air) vs the wavelength or amplitude of the soundwave?

Layer of drywall, layer of sheet steel (good for fireproofing) and a layer
of thick polystyrene (good for heat insulation) should be effective.
I'm not sure about the polystyrene though, it may be toxic in a fire.

High tech solution: have loudspeakers operate at the same frequency
but 180 degrees out of phase. This has been done in some cases
where an engine has been a source of noise. You pick up the sound
with a microphone, pass the electronic signal through a delay line and
then amplify it to drive the speakers.

| I also recognize that foam, blankets, and other softer substrates can absorb
| sound, but (other than layering them inside the wall) I'm trying to end up
| with clean interior design and would avoid them if possible.

No pain, no gain. Whatever you do will be a compromise. Sometimes
the cheapest and most effective solution is to throw rocks at your
neighbour's window and get them to move. This should only be used
as a last resort.

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Androcles, proud to be as British as Baldric.
http://www.androcles01.pwp.blueyonder.co.uk/MagnaCarta.wmv

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Natural Science Forum / Physics / General Physics / June 2008

Physics of sound waves (reflection vs transmission) question