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

$A$ steel rod $100 \; cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be $2.53 \; kHz$. What is the speed (in $km/s$) of sound in steel?

The speed of sound waves in a fluid depends upon:

The minimum audible wavelength at room temperature is about

If the frequency of a sound wave is $n$ and its velocity is $v$,what will be the new velocity if the frequency is changed to $4n$?

$A$ steel rod of length $100 \, cm$ is clamped at the middle. The frequency of the fundamental mode for the longitudinal vibrations of the rod is ..... $kHz$ (Speed of sound in steel $= 5 \, km \, s^{-1}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module