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

• A. \(\sqrt{\frac{m_1}{m_2}}\)
• B. \(\sqrt{\frac{m_2}{m_1}}\)
• C. \(\frac{m_1}{m_2}\)
• D. \(\frac{m_2}{m_1}\)

Hint:

Speed of sound in a gas is proportional to root of T over molar mass.

Answer 1

The Correct Option is B

Step 1: Approach
Relate the speed of sound to the rms molecular speed.

Step 2: Relation
Sound speed is proportional to the rms speed, which is $\sqrt{3RT/M}$. At equal $T$ and equal $\gamma$, speed is proportional to $M^{-1/2}$.

Step 3: Ratio
$\dfrac{v_1}{v_2}=\left(\dfrac{m_1}{m_2}\right)^{-1/2}=\sqrt{\dfrac{m_2}{m_1}}$. Option (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). \[ \boxed{\sqrt{\frac{m_2}{m_1}}} \]