Question:
Two monoatomic 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 gas '2' is
Two monoatomic 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 gas '2' is
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Speed of sound in a gas is proportional to root of T over molar mass.
Updated On: Oct 1, 2026
- \(\sqrt{\frac{m_1}{m_2}}\)
- \(\sqrt{\frac{m_2}{m_1}}\)
- \(\frac{m_1}{m_2}\)
- \(\frac{m_2}{m_1}\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
The speed of sound in an ideal gas is \(v=\sqrt{\dfrac{\gamma RT}{M}}\). Both gases are monatomic, so \(\gamma=\dfrac53\) for each. The temperature is the same.
Step 2: Ratio
\[ \frac{v_1}{v_2}=\sqrt{\frac{M_2}{M_1}}=\sqrt{\frac{m_2}{m_1}} \]
Step 3: Meaning
A heavier gas has a smaller speed of sound. Gas 1 with larger molecular mass \(m_1\) is slower, so the ratio has \(m_2\) on top.
Step 4: Check the options
Option (A) is the inverse. Options (C) and (D) lack the square root. So the answer is (B).
Final Answer:
At equal temperature the speed varies as one over root of molecular mass, so the ratio is root of m2 over m1, option (B). \[ \boxed{\sqrt{\frac{m_2}{m_1}}} \]
The speed of sound in an ideal gas is \(v=\sqrt{\dfrac{\gamma RT}{M}}\). Both gases are monatomic, so \(\gamma=\dfrac53\) for each. The temperature is the same.
Step 2: Ratio
\[ \frac{v_1}{v_2}=\sqrt{\frac{M_2}{M_1}}=\sqrt{\frac{m_2}{m_1}} \]
Step 3: Meaning
A heavier gas has a smaller speed of sound. Gas 1 with larger molecular mass \(m_1\) is slower, so the ratio has \(m_2\) on top.
Step 4: Check the options
Option (A) is the inverse. Options (C) and (D) lack the square root. So the answer is (B).
Final Answer:
At equal temperature the speed varies as one over root of molecular mass, so the ratio is root of m2 over m1, option (B). \[ \boxed{\sqrt{\frac{m_2}{m_1}}} \]
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