The velocity of sound is v_s in air. If the d | vedclass

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(A) The velocity of sound in a gas is given by the formula $v = \sqrt{\frac{\gamma P}{\rho}}$,where $\gamma$ is the adiabatic index,$P$ is the pressur

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$\frac{v_s}{2}$

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(A) The velocity of sound in a gas is given by the formula $v = \sqrt{\frac{\gamma P}{\rho}}$,where $\gamma$ is the adiabatic index,$P$ is the pressure,and $\rho$ is the density of the gas.Assuming the pressure $P$ remains constant,the velocity of sound is inversely proportional to the square root of the density: $v \propto \frac{1}{\sqrt{\rho}}$.Given the initial velocity is $v_s$ at density $\rho_1 = \rho$,and the new density is $\rho_2 = 4\rho$.Using the ratio: $\frac{v_{new}}{v_s} = \sqrt{\frac{\rho_1}{\rho_2}} = \sqrt{\frac{\rho}{4\rho}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.Therefore,the new velocity is $v_{new} = \frac{v_s}{2}$.

The velocity of sound is $v_s$ in air. If the density of air is increased to $4$ times,then the new velocity of sound will be

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