Enzo 13 Oct 2018

Question

A man stands between two walls. He clapped his hands once and hears two echoes – one after 0.500 s and the other 0.300 s after the first. If the speed of sound in air is 330 ms-1, what is the distance between the two walls?


Answer

The first echo comes from the sound that travels to the nearer wall and reflects back.

Enzo-20181013-1.jpg

The distance travelled by the sound is

Enzo-20181013-2.jpg


Since the sound travels twice the distance between the man and the nearer wall,

Enzo-20181013-3.jpg

The second echo comes from the sound that travels to the farther wall and reflects back.

Enzo-20181013-4.jpg

We can calculate the distance travelled by the sound and the distance between the man and the farther wall.

Enzo-20181013-5.jpg

Hence, the distance between the two walls can be found.

Enzo-20181013-6.jpg