MHT CET · Physics · Waves and Sound
Two monoatomic ideal gases A and B 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 A to that in gas B is given by
- A \(\sqrt{\frac{m_2}{m_1}}\)
- B \(\frac{\frac{m_2}{m_1}}{\sqrt{\frac{m_2}{m_1}}}\)
- C \(\sqrt{\frac{m_1}{m_2}}\)
- D \(\frac{m_2}{m_1}\)
Answer & Solution
Correct Answer
(A) \(\sqrt{\frac{m_2}{m_1}}\)
Step-by-step Solution
Detailed explanation
The speed of sound in a gaseous medium is given by, \(v=\sqrt{\frac{\gamma R T}{m}}\), where \(y\) is the ratio of \(\frac{C_P}{C_v}, R\) is the universal gas constant, \(m\) is the molecular weight of the gas and \(T\) is the temperature of the gas.
Therefore, \(v \propto \frac{1}{\sqrt{m}}\)
\(\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{m_2}{m_1}}\)
Therefore, \(v \propto \frac{1}{\sqrt{m}}\)
\(\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{m_2}{m_1}}\)
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