Question

At room temperature , velocity of sound in air at 10 atmospheric pressure and at 1 atmospheric pressure will be in the ratio :

• A. 10:1
• B. 1:10
• C. 1:1
• D. cannot say

Answer 1

The correct option is C 1:1

Speed of sound in air can be given by

$v=\sqrt{\frac{\gamma P}{\rho }}$, ...(1)

where $\gamma$ is the adiabatic index, P is the air pressure and $\rho$ is air density.

Now at constant temperature, P can be replaced by $nRT/V$ and $\rho$ by $nM/V$.

Thus Eq. (1) becomes

$v=\sqrt{\frac{\gamma RT}{M}}$, ...(2)

where R is molar gas constant and M is molar mass.

Hence, at constant temperature, v is independent of gas pressure.