Numerical problems on Echo of sound

Question 1: A person clapped his hands near a cliff and heard an echo after 2 seconds. What is the distance of the cliff from the person if the speed of the sound, v is taken as 346 m/s?

Solution:

Given,
Speed of sound, v = 346 m/s
Time taken to hear the echo, t = 2 s
Distance traveled by the sound = v × t = 346 m/s × 2 s = 692 m
In 2 seconds sound has to travel twice the distance between the cliff and the person. Hence, the distance between the cliff and the person = 692/2 m= 346 m.

Question 2: An echo is heard in 3 s. What is the distance of the reflecting surface from the source, given that the speed of sound is 342 m/s?

Solution:

Given,
Speed of sound, v = 342 m/s
Time taken to hear the echo, t = 3 s
Distance traveled by the sound = v × t = 342 m/s × 3 s = 1026 m

In 3 seconds sound has to travel twice the distance between the source and the reflecting surface.
Hence, the distance of the reflecting surface from the source = 1026/2 m= 513 m.