Question

The velocity of sound in a medium at a certain temperature is 'V'. If the absolute temperature of the medium is increased by 44% then find the percentage change in the velocity of the sound.

• A. 10
• B. 20
• C. 30
• D. 40

Answer 1

The correct option is B 20

We know that Speed of Sound in a Gas is, $V=(\gamma RT/M{)}^{1/2}$ , where $v$ is the speed of sound in that gas, $\gamma$ is the adibatic index, $R$ is universal gas constant, $T$ is temperature and $M$ is the molecular weight of the given gas.

Now if only temperature is changed and all conditions remain same then, $V\propto T^{1/2}$

Now increase of temperature is 44% , Therefor we get $T_0=T+44/100\ast T\cong 144/100\ast T$

Therefor, $V_0=T_0^{1/2}\cong 144/100\ast T^{1/2}=1.2V$

Therefor we get increase of $V_o-V=0.2V$

% Increase is , $0.2V/V\ast 100=20$%

Therefor we get a increase of $20$% in Temperature.