Physics - Sound Wave Question with Solution | TestHub

The speed of sound in an ideal gas is given by $v=\sqrt{\frac{\gamma RT}{M}}$, where $M$ is the molar mass of the gas.

Since $M=m{N}_A$, where $m$ is the molecular mass and $N_A$ is Avogadro's number, the speed of sound can be written as $v=\sqrt{\frac{\gamma RT}{m{N}_A}}$.

Both gases are monoatomic, so they have the same adiabatic index $\gamma$. They are also at the same temperature $T$.

Therefore, $v\propto \frac{1}{\sqrt{m}}$.

The ratio of the speed of sound in gas '1' to that in gas '2' is $\frac{v_1}{v_2}=\sqrt{\frac{m_2}{m_1}}$.

Answer: $\sqrt{\frac{m_2}{m_1}}$