Assertion : The change in air pressure affect | vedclass

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

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If both the Assertion and Reason are incorrect.

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(D) The speed of sound in a 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.According to the ideal gas law,$PV = nRT$,which can be written as $P = \frac{\rho RT}{M}$,where $M$ is the molar mass.Thus,the ratio $\frac{P}{\rho} = \frac{RT}{M}$.Substituting this into the speed formula,we get $v = \sqrt{\frac{\gamma RT}{M}}$.Since $R$,$T$,and $M$ are constant at a given temperature,the speed of sound $v$ is independent of pressure $P$.Therefore,the Assertion is incorrect because pressure change does not affect the speed of sound at a constant temperature.The Reason is also incorrect because the speed of sound is independent of pressure,not proportional to its square.Thus,both the Assertion and Reason are incorrect.

$Assertion :$ The change in air pressure affects the speed of sound.
$Reason :$ The speed of sound in gases is proportional to the square of pressure.

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$Assertion :$ The change in air pressure affects the speed of sound.$Reason :$ The speed of sound in gases is proportional to the square of pressure.