The speed of sound in air at temperature T an | 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 $v = \sqrt{\frac{\gamma R T}{M}}$.From this relation, it is clear that the speed of sou

Vedclass · Accepted Answer

$\sqrt{2} v$

Vedclass · Answer

(C) The speed of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma R T}{M}}$.From this relation, it is clear that the speed of sound $v$ is independent of pressure $p$ and is directly proportional to the square root of the absolute temperature $T$, i.e.,$v \propto \sqrt{T}$.Given initial conditions: $T_1 = T$ and $v_1 = v$.Given final conditions: $T_2 = 2 T$ and $p_2 = \frac{p}{2}$.Since $v$ is independent of pressure, the change in pressure does not affect the speed.Using the proportionality $v \propto \sqrt{T}$, we have:$\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$$\frac{v_2}{v} = \sqrt{\frac{2 T}{T}} = \sqrt{2}$Therefore, $v_2 = \sqrt{2} v$.

The speed of sound in air at temperature $T$ and pressure $p$ is $v$. When the temperature is increased to $2 T$ and the pressure is reduced to $\frac{p}{2}$, then the speed is changed to

Similar Questions

Which one of the following statements is true?

$A$ metal rod of $1 \; m$ length is dropped vertically onto a hard metal floor. Using an oscilloscope,it is determined that the impact produces a longitudinal wave of $1.2 \; kHz$ frequency. The speed of sound in the metal rod is: (in $; m/s$)

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

Which of the following cannot be polarised?

$A$ person standing on an open ground hears the sound of a jet aeroplane coming from the north at an angle of $60^{\circ}$ with the ground level. However,he finds the aeroplane right vertically above his position. If $\upsilon$ is the speed of sound,what is the speed of the plane?

Vedclass Test Series

Exam Paper Generator

Online Exam Module