Q.

The speed of sound in a gas is V and the root mean square speed of gas molecules is vrms.  If the ratio of the specific heats of gas γ=1.5 then ratio v/vrms is

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a

1:3

b

1:4

c

1:2

d

1:2

answer is C.

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Detailed Solution

Root Mean Square Velocity : Vrms=3Pρ Speed of sound in a gas : V=γPρ ∴VVrms=γ3=1.53=12
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The speed of sound in a gas is V and the root mean square speed of gas molecules is vrms.  If the ratio of the specific heats of gas γ=1.5 then ratio v/vrms is