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Question

The speed of sound in a gas is $$V$$. If the rms velocity of gas molecules is C$$_{rms}$$ then the value of $$\displaystyle \frac{V}{\quad C_{rms}}$$ will be


A
3γ
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B
γ3
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C
3γ
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D
γ3
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Solution

The correct option is B $$\displaystyle \sqrt{\frac{\gamma}{3}}$$
Speed of sound $$V = \sqrt{\dfrac{\gamma RT}{M}}$$
rms velocity of gas molecules $${C}_{rms} = \sqrt{3\dfrac{RT}{M}}$$
$$\dfrac{V}{{C}_{rms}} = \sqrt{\dfrac{\gamma}{3}}$$
Answer is D.

Physics

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