# Is there a theortical limit to the amount of sound-energy air can contain?

is there a theoretical limit to the amount of sound energy air can contain? In case, there is a limit, what is that limit?

-
@Georg I don't see what the point of that comment is. That's pretty close to the kind of inappropriate comments you've been warned about in the past... –  David Z Oct 18 '11 at 17:52
I actually think it's a fun question. It depends what configurations of the air you're ready to call sound. For example, you may allow sound waves that make the air pressure drop everywhere except for $1/N$ of the volume. I guess that the work this system may perform while switching to the uniform pressure goes like $C.p_{\rm average}V_{\rm total}\ln(N)$ or so. Of course, if you may compress all the air to very small regions, you will get more energy. Then there are lots of questions whether you allow heat (hot air), phase transitions, hot air, nuclear reactions etc. –  Luboš Motl Oct 18 '11 at 19:10

## 1 Answer

The answer depends on the pressure of the air, and as the comments point out the sound source. An extreme (theoretical max) loud sound source would pull basically a vacuum in the troughs and a double over pressure in the peak. It would seem that 1/N only makes sense for N=2, if the sound is to be considered more than just a single shot.

So you would calculate it in joules per metre**3 by working out something like the energy stored in air when you compress it by a factor of two. Pressure is 100kPa so to get to 200 kPa over a distance of 1/2 a metre would work out to 150kPa*0.5m*1m**2 = ...

Getting sound that loud is mechanically quite a trick, so if I wanted a real answer, I would scrub the net for the highest spl recorded and work from that. Like 160 dB?

-
google.ca/search?q=150kPa*0.5m*1m**2&ie=UTF-8 –  Tom Andersen Oct 18 '11 at 22:32
Sorry the paste of the URL is not working. If you copy and paste the energy calculation into google you get 75,000 Joules per cubic meter. –  Tom Andersen Oct 18 '11 at 22:34
sengpielaudio.com/calculator-soundlevel.htm looks really good. –  Tom Andersen Oct 18 '11 at 22:54