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

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

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 $

Vedclass · Accepted Answer

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

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

Similar Questions

Two monoatomic ideal gases $1$ and $2$ of molecular masses $m_1$ and $m_2$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas $1$ to that in gas $2$ is given by

Sound velocity is maximum in

The speed of sound in mercury at a certain temperature is $1450 \, m/s$. Given the density of mercury as $13.6 \times 10^3 \, kg/m^3$,the bulk modulus for mercury is:

Velocity of sound is maximum in

When a tuning fork vibrates,the waves produced in the fork are

Vedclass Test Series

Exam Paper Generator

Online Exam Module