The temperature at which the speed of sound i | vedclass

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

Question

(C) 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,$R$ is the gas c

Vedclass · Accepted Answer

$927$

Vedclass · Answer

(C) 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,$R$ is the gas constant,$T$ is the absolute temperature in Kelvin,and $M$ is the molar mass of the gas.From this relation,we can see that $v \propto \sqrt{T}$.Let $v_1$ be the speed of sound at temperature $T_1$ and $v_2$ be the speed at $T_2$.Given $T_1 = 27^\circ C = 27 + 273 = 300 \ K$.We want the speed to be doubled,so $v_2 = 2v_1$.Using the proportionality $v_2/v_1 = \sqrt{T_2/T_1}$,we get $2 = \sqrt{T_2/300}$.Squaring both sides,$4 = T_2/300$,which gives $T_2 = 1200 \ K$.Converting back to Celsius,$T_2 = 1200 - 273 = 927^\circ C$.

The temperature at which the speed of sound in air becomes double of its value at $27^\circ C$ is ... $^\circ C$

Similar Questions

$A$ source of frequency $f$ is emitting sound waves. If the temperature of the medium increases,then

Two monoatomic ideal gases $A$ and $B$ 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 $A$ to that in gas $B$ is given by

For a particular sound wave propagating in air, a path difference between two points is $0.54 \, m$ which is equivalent to a phase difference of $(1.8 \pi)$. If the velocity of the sound wave in air is $330 \, m/s$, the frequency of this wave is: (in $Hz$.)

What is the effect of pressure on the speed of sound in a medium,if pressure is doubled at constant temperature?

At what temperature will the speed of sound be nearly $1.5$ times its value at $N.T.P.$ (in $^{\circ} C$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module