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(A) The speed of sound $v$ in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma P}{\rho}}$,where $P$ is the pressure and $\rho$ is the dens

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Remains same

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(A) The speed of sound $v$ in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma P}{\rho}}$,where $P$ is the pressure and $\rho$ is the density of the gas.Since density $\rho = \frac{m}{V}$ and for an ideal gas $PV = nRT$,we have $\rho = \frac{PM}{RT}$,where $M$ is the molar mass.Substituting this into the speed formula: $v = \sqrt{\frac{\gamma P}{PM/RT}} = \sqrt{\frac{\gamma RT}{M}}$.As seen from the final expression,the speed of sound depends only on temperature $T$ and the nature of the gas (molar mass $M$ and adiabatic index $\gamma$).Therefore,at a constant temperature,the speed of sound is independent of the pressure. If the pressure is doubled,the speed of sound remains the same.

What is the effect of pressure on the speed of sound in a medium,if pressure is doubled at constant temperature?

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