Speed of Sound in Gases

Problems from IIT JEE

Problem (IIT JEE 2000): Two monatomic ideal gases 1 and 2 of molecular masses $m_1$ and $m_2$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in the gas 2 is given by,

  1. $\sqrt{\frac{m_1}{m_2}}$
  2. $\sqrt{\frac{m_2}{m_1}}$
  3. $\frac{m_1}{m_2}$
  4. $\frac{m_2}{m_1}$

Solution: The speed of sound in a gas with molecular mass $M$ and kept at temperature $T$ is given by, \begin{align} \label{ipa:eqn:1} v=\sqrt{\gamma RT/M}. \end{align} For the given monatomic gases, $\gamma_1=\gamma_2=5/3$ and temperature $T_1=T_2$. Substitute in above equation to get, \begin{align} {v_1}/{v_2}=\sqrt{M_2/M_1}=\sqrt{m_2/m_1}.\nonumber \end{align}