Speed of sound in oxygen (O₂) at a certain temperature is 460, ms^{-1} . speed of sound in helium

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14.Waves and Sound

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The speed of sound in oxygen $(O_2)$ at a certain temperature is $460\, ms^{-1}$. The speed of sound in helium $(He)$ at the same temperature will be ............. $\mathrm{m/s}$ (assume both gases to be ideal)

A

$1420$

B

$500$

C

$650$

D

$330$

Solution

Speed of sound is given by : $\mathrm{v}=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}}$

$\mathrm{v}_{\mathrm{O}_{2}}=\sqrt{\frac{\frac{7}{5} \mathrm{RT}}{32}}$ and $\mathrm{v}_{\mathrm{He}}=\sqrt{\frac{\frac{5}{3} \mathrm{RT}}{4}}$

$\frac{v_{O_{2}}}{v_{H e}}=\sqrt{\frac{7 \times 3 \times 4}{5 \times 32 \times 5}}$

or $\quad {{\rm{v}}_{{\rm{He}}}} = 460 \times 10 \times \sqrt {\frac{2}{{21}}} \simeq 1420\,\,{\rm{m}}/{\rm{s}}$

Standard 11

Physics

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