Question

If the pressure, temperature and density of an ideal gas are denoted by $P,T$ and $\rho$, respectively, the velocity of sound in the gas is

• A. Proportional to $\sqrt{P}$, when $T$ is constant
• B. Proportional to $\sqrt{T}$
• C. Proportional to $\sqrt{P}$, when $\rho$ is constant
• D. Proportional to $T$

Answer 1

Answer: (B), (C)

Proportional to $\sqrt{T}$
Proportional to $\sqrt{P}$, when $\rho$ is constant

From kinetic theory of gas, we can write

$v=\sqrt{\frac{\gamma RT}{M}}=\sqrt{\frac{\gamma P}{\rho }}$

From the given formula it is clear that, the velocity of the sound in the gas is proportional to $\sqrt{T}$ and $\sqrt{P}$ when $\rho$ is constat.