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Q.
If at STP, velocity of sound in a gas $(\gamma=1.5)$ is $600 \,m / s$, the r.m.s. velocity of the gas molecules at STP will be
Waves
Solution:
Velocity of sound $=\sqrt{\frac{\gamma R T}{M}}$
RMS speed $=\sqrt{\frac{3 R T}{M}}$
$\frac{v_{s}}{r_{r m s}}=\sqrt{\frac{\gamma}{3}}$
$\frac{v_{s}}{r_{ rms }}=\sqrt{\frac{1}{2}}$
$v_{ mms }=600 \sqrt{2}\, m / s$