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what is the relationship of sound volume to atmospheric pressure? if I was in a plane with a cabin pressure equal to 8000 feet would the volume drop be noticable?

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also see here: physics.stackexchange.com/questions/672/… –  troyaner Aug 14 '11 at 18:24

1 Answer 1

There is not going to be any generic answer to your question.

Suppose I drop a book on the floor, and the book hits the floor with 1 joule of kinetic energy. Let's assume that there is very little internal friction in the book or the floor, so that none of the energy can be dissipated into heat, and that the floor is very stiff, so that no energy can be transmitted as vibrations in the floor. Then by conservation of energy, the amount of sound energy is going to be exactly 1 joule. This argument is independent of whether this is the floor of my house, near sea level, or the deck of an airplane. It only depends on the assumption that the mechanisms for dissipating energy into heat and vibration are much less efficient than the mechanism for dissipating it into sound waves in the air.

On the other hand, let's say for the sake of argument that in a hand clap at sea level, 1/3 of the energy goes into sound, 1/3 into vibrations transmitted down through the arms, and 1/3 into heating in the palms. In an airplane, these 1:1:1 proportions will be altered, because the conversion of energy into sound waves in air will be less efficient. Because the competition among the three dissipative processes is fairly equal, there will be a big reduction in loudness when the pressure is low.

So the answer is that it depends completely on the details of the process of production of the sound waves.

In the extreme case, suppose you do these experiments in outer space. Outer space is not a perfect vacuum, so it can support sound waves. However, the efficiency of the coupling to sound waves is extremely low, so almost any other mechanism for dissipating the energy will be many orders of magnitude more efficient.

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