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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$\frac{v_s}{2}$

Vedclass · Answer

(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

Similar Questions

The velocity of sound in air is:

Derive the expression for the speed of a sound wave and obtain the equations for the speed of sound in different media.

What is the velocity of a wave in a monoatomic gas having a pressure of $1 \, kPa$ and a density of $2.6 \, kg/m^3$?

$A$ wave with a wavelength of $0.60 \ cm$ is produced in air and it travels at a speed of $300 \ ms^{-1}$. This wave is classified as:

Sound waves travel at $350 \ m/s$ through warm air and at $3500 \ m/s$ through brass. The wavelength of a $700 \ Hz$ acoustic wave as it enters brass from warm air:

Vedclass Test Series

Exam Paper Generator

Online Exam Module