Two friends A and B are standing a distance x apart in an open field and wind is blowing from A to B. A beats a drum and B hears the sound t 1 time after he sees the event. An and B interchange their positions and the experiment is repeated. This time B hears the drum t 2 time after he sees the event. Calculate the velocity of sound in still air u and the velocity of wind u. Neglect the time light takes in travelling between the friends.

Question

Philoid · Accepted Answer

Given:
Distance between A and B = x
Velocity of sound in air = v
Velocity of wind = u

First Case:
When A beats the drum from his original position:

Resultant velocity of sound = u + v
Here, is the time at which the sound of the drum is heard by B.

⇒ ----------- (i)

Second Case:
After interchanging the positions:
Resultant velocity of sound = v − u
∴

⇒ ------------- (ii)

From (i) and (ii), we get:

From (i), we get:

Putting the value of v in the above equation, we get:

∴ Velocity of sound,

Velocity of wind,