Question

The velocities of sound at the same temperature in two monoatomic gases of densities $p_1$ and $p_2$ are $v_1$ and $v_2$ respectively. If $p_1/p_2=4$, then the value of $v_1/v_2$ is

• A. $\frac{1}{4}$
• B. $2$
• C. $\frac{1}{2}$
• D. $4$

Answer 1

Answer: (A), (C)

The correct options are
A $\frac{1}{4}$
C $\frac{1}{2}$

For velocity of sound in gas
$v=\sqrt{\frac{p\gamma }{p}}$
$[P$ is pressure and $p$ is density of gas, $\gamma$ is $C_p/C_v]$
Here, $v_1=\sqrt{\frac{\gamma P}{p_1}}$ and $v_2=\sqrt{\frac{\gamma P}{p_2}}$
$\frac{v_1}{v_2}=\sqrt{\frac{p_2}{p_1}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$