A man stands in front of a large wall at a distance of 50.0 m and claps his hands at regular intervals. Initially, the interval is large. He progressively reduces the interval, fixing it at a value where the echo of a clap merges with the subsequent clap. If he claps 10 times during every 3 seconds, determine the velocity of sound in air.

Step-by-step solution

Let the distance of the man from the wall be d = 50.0 m . The sound of the clap travels to the wall and reflects back to the man. The total distance traveled by the sound to hear the echo is 2d = 100 m . Let the velocity of sound be v . The time taken for the echo to reach the man is: t = 2d v The man progressively reduces the time interval between claps until the echo of a clap merges exactly with the subsequent clap. This means the time taken for the echo to return is exactly equal to the time interval between tw