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Q. If the temperature of gas remains constant then prove that there is no effect of the pressure change on the speed of sound.

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Solution

Dear Student
If the temperature of the gas remains constant, then by Boyle’s law PV = constant

That is, P (m/ρ) = constant

p/ρ is a constant, when mass (m) of a gas is constant. If the pressure changes from P to P ′ then the corresponding density also will change from ρ to ρ ′ such that P/ρ is a constant.

In Laplace’s formula √(γP/ρ) is also a constant. Therefore the velocity of sound in a gas is independent of the change in pressure provided the temperature remains constant.
Regards

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Solve this: Q. If the temperature of gas remains constant then prove that there is no effect of the pressure change on the speed of sound.

Solve this:
Q. If the temperature of gas remains constant then prove that there is no effect of the pressure change on the speed of sound.