First slide

Speed of wave

Question

The time taken by sound waves to travel the distance l if the air temperature between them varies linearly from $T_{1} to T_{2}$ (velocity of sound in air is given by $v = α \sqrt{T}$ )

Difficult

A

$\frac{2 l}{α (\sqrt{T_{2}} + \sqrt{T_{1}})}$
B

$\frac{2 l}{α (\sqrt{T_{2}} - \sqrt{T_{1}})}$
C

$\frac{l}{α (\sqrt{T_{2}} + \sqrt{T_{1}})}$
D

$\frac{l}{α (\sqrt{T_{2}} - \sqrt{T_{1}})}$

Solution

$T = T_{1} + (T_{2} - T_{1}) \frac{x}{l} ∴ \frac{dx}{d T} = \frac{l}{T_{2} - T_{1}} t = \int \frac{dx}{v} = \int_{T_{1}}^{T_{2}} \frac{l}{T_{2} - T_{1}} \frac{dT}{α \sqrt{T}} = \frac{l}{(T_{2} - T) α} 2 (\sqrt{T_{2}} - \sqrt{T_{1}}) = \frac{2 l}{α (\sqrt{T_{2}} + \sqrt{T_{1}})}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App