Question

A man standing between two cliffs fires a gun and hears an echo after every one second. The distance of the man from the nearest cliff is 170 m, calculate:

1. velocity of sound,
2. distance between two cliffs.

Answer 1

The echo from the nearer cliff is heard after 1 s. Since sound travels to the cliff and back, the distance travelled is twice the distance to the cliff.

(i) Velocity of sound:

\[v=\frac{2d}{t}\]

\[=\frac{2\times170}{1}\]

= 340 ms⁻¹

The echo from the farther cliff is heard 1 s later, i.e. 2 s after the gun is fired. Thus, the distance to the farther cliff is:

\[d_{2}=\frac{vt}{2}\]

\[=\frac{340\times2}{2}\]

= 340 m

(ii) Distance between the cliffs = 170 + 340 = 510 m