Pressure Wave from Rapid Balloon Expansion

[firedancer414]

Hello physics forum,

I'm interested in modeling the pressure wave created due to the rapid inflation of a balloon. Say I'm able to rapidly increase the temperature of the air in a balloon, faster than it can equilibrate its pressure with the outside air. It will expand to satisfy PV = T, and radiate a pressure wave. I'm interested in calculating the frequency power spectra of this pressure wave.

What is the best way to solve for this? One way I can think of is to solve for the velocity of the balloon membrane as it expands, but I'm not sure how I would calculate the membrane velocity. I also thought that I might just be able to use the pressure wave Green's function, and integrate that over the volume of increased pressure.

Please help! Thanks =)

 

[firedancer414]

Upon further reflection, this bears resemblance to a shock wave. With this context in mind, is there some simple solution?

I work primarily with optics, I feel like a fish out of water! References, anything would be much appreciated =)

 

[Bob S]

Read about Fermi's measurement of the Trinity Site blast in
http://www.cfo.doe.gov/me70/manhattan/trinity.htm
"Probably the most mundane response of all was Fermi's: he had calculated ahead of time how far the blast wave might displace small pieces of paper released into it. About 40 seconds after the explosion, Fermi stood, sprinkled his pre-prepared slips of paper into the atomic wind, and estimated from their deflection that the test had released energy equivalent to 10,000 tons of TNT. "
fermi was about 10,000 meters away.