Two monoatomic ideal gases '1' and '2' of mol | vedclass

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

Question

(B) The speed of sound $v$ in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$, where $\gamma$ is the adiabatic index, $R$ is the

Vedclass · Accepted Answer

$\sqrt{\frac{m_2}{m_1}}$

Vedclass · Answer

(B) The speed of sound $v$ in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$, where $\gamma$ is the adiabatic index, $R$ is the universal gas constant, $T$ is the absolute temperature, and $M$ is the molar mass of the gas.For monoatomic gases, the adiabatic index $\gamma$ is the same for both gases, i.e.,$\gamma = 5/3$.Since both gases are kept at the same temperature $T$, the ratio of the speed of sound in gas '$1$' $(v_1)$ to that in gas '$2$' $(v_2)$ is:$\frac{v_1}{v_2} = \frac{\sqrt{\frac{\gamma RT}{m_1}}}{\sqrt{\frac{\gamma RT}{m_2}}}$$\frac{v_1}{v_2} = \sqrt{\frac{m_2}{m_1}}$Thus, the ratio of the speed of sound in gas '$1$' to that in gas '$2$' is $\sqrt{\frac{m_2}{m_1}}$.

Column - $A$	Column - $B$
$(a)$ Speed of longitudinal waves in gas and liquid.	$(i)$ $v = \sqrt{\frac{B}{\rho}}$
$(b)$ Speed of longitudinal waves in solid rod.	$(ii)$ $v = \sqrt{\frac{Y}{\rho}}$
$(c)$ Speed of sound in air according to Newton.	$(iii)$ $v = \sqrt{\frac{P}{\rho}}$
$(d)$ Speed of sound in air according to Laplace.	$(iv)$ $v = \sqrt{\frac{\gamma P}{\rho}}$

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

Similar Questions

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

Velocity of sound in vacuum is .... $ms^{-1}$

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:

What is the ratio of the velocity of sound in hydrogen $\left(\gamma=\frac{7}{5}\right)$ to that in helium $\left(\gamma=\frac{5}{3}\right)$ at the same temperature? (Molecular weight of hydrogen and helium is $2$ and $4$ respectively)

Vedclass Test Series

Exam Paper Generator

Online Exam Module