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(C) The velocity of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma R T}{M}} = \sqrt{\frac{\gamma p}{\rho}}$.$(i)$ From the rela

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proportional to $\sqrt{p}$,when $\rho$ is constant.

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(C) The velocity of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma R T}{M}} = \sqrt{\frac{\gamma p}{\rho}}$.$(i)$ From the relation $v = \sqrt{\frac{\gamma R T}{M}}$,it is clear that the velocity of sound is proportional to the square root of the absolute temperature,i.e.,$v \propto \sqrt{T}$.(ii) From the relation $v = \sqrt{\frac{\gamma p}{\rho}}$,if the density $\rho$ is kept constant,the velocity of sound is proportional to the square root of the pressure $p$,i.e.,$v \propto \sqrt{p}$.Comparing these with the given options,both $B$ and $C$ are physically correct statements based on the derived relations.

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

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