The ratio of the speed of sound in helium gas | vedclass

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

Question

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

Vedclass · Accepted Answer

$\frac{5}{\sqrt{3}}$

Vedclass · Answer

(D) The speed of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$, where $\gamma$ is the adiabatic index (ratio of specific heats), $R$ is the universal gas constant, $T$ is the temperature, and $M$ is the molar mass.Given $T = 295 	ext{ K}$ for both gases, the ratio of the speed of sound in helium $(v_{He})$ to nitrogen $(v_{N_2})$ is:$\frac{v_{He}}{v_{N_2}} = \sqrt{\frac{\gamma_{He} R T / M_{He}}{\gamma_{N_2} R T / M_{N_2}}} = \sqrt{\frac{\gamma_{He}}{\gamma_{N_2}} \cdot \frac{M_{N_2}}{M_{He}}}$Substituting the given values: $\gamma_{He} = 5/3$, $\gamma_{N_2} = 7/5$, $M_{He} = 4$, $M_{N_2} = 28$.$\frac{v_{He}}{v_{N_2}} = \sqrt{\frac{5/3}{7/5} \cdot \frac{28}{4}} = \sqrt{\frac{5}{3} \cdot \frac{5}{7} \cdot 7} = \sqrt{\frac{25}{3}} = \frac{5}{\sqrt{3}}$.

The ratio of the speed of sound in helium gas to that in nitrogen gas at $295 \text{ K}$ is (Ratio of specific heats for helium is $5/3$ and that for nitrogen is $7/5$. Molecular weight for helium and nitrogen are $4$ and $28$ respectively.)

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 of sound in steel? (in $km/s$)

The echo of a gun shot is heard $8 \, s$ after the gun is fired. How far from the shooter is the surface that reflects the sound (in $, m$)? (Velocity of sound in air $= 350 \, m/s$)

The ratio of the velocity of sound in hydrogen gas $(\gamma = 7/5)$ to that in helium gas $(\gamma = 5/3)$ at the same temperature is

$A$ man,standing between two cliffs,claps his hands and starts hearing a series of echoes at intervals of one second. If the speed of sound in air is $340 \, ms^{-1}$,the distance between the cliffs is .... $m$

$A$ source $S$ of frequency $f_0$ and an observer $O$,moving with speeds $v_1$ and $v_2$ respectively,are moving away from each other. When they are separated by a distance $a$ at $t = 0$,a pulse is emitted by the source. This pulse is received by $O$ at time $t_1$. Then $t_1$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module