Two monoatomic ideal gases 1 and 2 of molecular masses M₁ and M₂ respectively are enclosed in se

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14.Waves and Sound

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Two monoatomic ideal gases $1$ and $2$ of molecular masses $M_1$ and $M_2$ respectively are enclosed in separate containers kept a 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

$\frac{{{M_2}}}{{{M_1}}}$

Solution

$\mathrm{v}_{\mathrm{s}}=\sqrt{\frac{\mathrm{rRT}}{\mathrm{M}}} \Rightarrow \mathrm{v}_{\mathrm{s}} \propto \sqrt{\frac{1}{\mathrm{M}}}$

$\Rightarrow \frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}=\sqrt{\frac{\mathrm{M}_{2}}{\mathrm{M}_{1}}}$

Standard 11

Physics

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