WBJEE · Physics · Waves and Sound
If the pressure, temperature and density of an ideal gas are denoted by \(p, T\) and \(\rho\), respectively, the velocity of sound in the gas is
- A proportional to \(\sqrt{p},\) when \(T\) is constant.
- B proportional to \(\sqrt{T}\)
- C proportional to \(\sqrt{p}\), when \(\rho\) is constant.
- D proportional to \(T\).
Answer & Solution
Correct Answer
(C) proportional to \(\sqrt{p}\), when \(\rho\) is constant.
Step-by-step Solution
Detailed explanation
\(v=\sqrt{\frac{\gamma R T}{M}}=\sqrt{\frac{\gamma P}{\rho}}\) (i) Velocity of sound is proportional to \(\sqrt{T}\) \(\therefore\) \(v \propto \sqrt{T}\) (ii) When \(\rho\) is constant, the velocity of sound is proportional to root of pressure \(P\) \(\therefore\)…
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