Consider the following statements in respect of sound waves:
I. The speed of sound waves decreases with an increase in temperature if the atmospheric pressure remains the same.
II. The speed of sound waves increases with increasing humidity if the atmospheric pressure remains the same.
III. The speed of sound waves is not affected by a change in atmospheric pressure, provided the temperature is kept constant.
Which of the statements given above are correct?

Question

Consider the following statements in respect of sound waves:

I. The speed of sound waves decreases with an increase in temperature if the atmospheric pressure remains the same.

II. The speed of sound waves increases with increasing humidity if the atmospheric pressure remains the same.

III. The speed of sound waves is not affected by a change in atmospheric pressure, provided the temperature is kept constant.

Which of the statements given above are correct?

Prepp Team · Accepted Answer

The speed of sound in a gas is $v=\sqrt{\dfrac{\gamma RT}{M}}$, which increases (not decreases) with temperature, so statement I is incorrect. Moist air has a lower average molar mass $M$ than dry air (water vapour, $M=18$, is lighter than the average of dry air, $M\approx29$), so increasing humidity increases the speed of sound at constant pressure; statement II is correct. Since $v=\sqrt{\gamma RT/M}$ does not contain pressure explicitly, and at constant temperature $P/\rho$ stays constant for an ideal gas, the speed of sound is unaffected by a pressure change alone; statement III is correct. Hence II and III only are correct. The correct option is (b).