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BITSAT 2023Paper 1

Exam: BITSAT
Year: 2023
Paper: Paper 1
Subject: Physics
Chapter: Waves and Sound

BITSAT 2023 · Paper 1 · Physics · Waves and Sound

The ratio of speed of sound in hydrogen gas to the speed of sound...

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

Options

A $4: 1$
B $1: 2$
C $1: 4$
D $1: 1$

Correct answer

A. $4: 1$

Step-by-step solution

Given

\mathrm{M}_{\mathrm{H}_2}=2 ; \mathrm{M}_{\mathrm{O}_2}=32

Speed of sound,

\mathrm{v}=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}}

\Rightarrow \quad v \propto \frac{1}{\sqrt{M}}

\therefore \quad \frac{\mathrm{v}_{\mathrm{H}_2}}{\mathrm{v}_{\mathrm{O}_2}}=\sqrt{\frac{\mathrm{M}_{\mathrm{O}_2}}{\mathrm{M}_{\mathrm{H}_2}}}=\sqrt{\frac{32}{2}}=4: 1

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