Discussion
Velocity of sound in air does not depend on
Answer: C
The speed of sound in air does not depend on the Pressure of air.
For an ideal gas the speed of sound is
\[ \begin{aligned} v &= \sqrt{\frac{\gamma P}{\rho}} \\ &= \sqrt{\frac{\gamma R T}{M}} \end{aligned} \]
If the pressure rises at constant temperature, the density rises in the same proportion, so the ratio \(P/\rho\) and the speed stay the same. The speed therefore depends on temperature, not on pressure.
Density matters when it changes independently, and temperature raises the speed by about 0.6 m/s per degree Celsius. Humidity matters too: moist air is less dense than dry air at the same temperature and pressure, so sound travels slightly faster in it.
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