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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 =)