The velocity of sound in a gas at pressure P | vedclass

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Question

(A) According to the Laplace correction for the speed of sound in an ideal gas,the velocity $v$ is given by $v = \sqrt{\frac{\gamma P}{\rho}}$,where $

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$v = \sqrt {\frac{\gamma P}{d}}$

Vedclass · Answer

(A) According to the Laplace correction for the speed of sound in an ideal gas,the velocity $v$ is given by $v = \sqrt{\frac{\gamma P}{\rho}}$,where $\gamma$ is the adiabatic index,$P$ is the pressure,and $\rho$ is the density.Given that the density is denoted by $d$,the formula becomes $v = \sqrt{\frac{\gamma P}{d}}$.This can be derived from the ideal gas equation $PV = nRT$,where $n = \frac{m}{M}$.Thus,$PV = \frac{m}{M}RT$,which implies $P = \frac{m}{V} \cdot \frac{RT}{M} = d \cdot \frac{RT}{M}$.Therefore,$\frac{P}{d} = \frac{RT}{M}$.Substituting this into the expression $v = \sqrt{\frac{\gamma RT}{M}}$,we get $v = \sqrt{\frac{\gamma P}{d}}$.

The velocity of sound in a gas at pressure $P$ and density $d$ is

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