Question

A person standing between two vertical cliffs and 480 m from the nearest cliff shouts. He hears the first echo after 3s and the second echo 2s later. Calculate:

1. The speed of sound.
2. The distance of the other cliff from the person

Answer 1

Given: Distance of nearest cliff, \(d_1 = 480\ \text{m}\)

Time for first echo, \(t_1 = 3\ \text{s}\)

(i) For an echo, sound travels to the cliff and back:

\[ v=\frac{2d_1}{t_1} \]

\[ v=\frac{2\times480}{3}\]

\[ {v=320\ \text{m/s}} \]

(ii) The second echo is heard 2 s after the first echo.

\[ t_2=3+2=5\ \text{s} \]

Let the distance of the other cliff be \(d_2\).

\[ d_2=\frac{vt_2}{2} \]

\[ d_2=\frac{320\times5}{2}\]

\[{d_2=800\ \text{m}} \]