Question

A person standing between two vertical cliffs and $480\mathrm{m}$ from the nearest cliff shouts. He hears the first echo after $3\mathrm{s}$ and the second echo $2\mathrm{s}$ later. Calculate the speed of sound.

Answer 1

Step 1: Given data

$D_1$ is the distance of the person from the nearest cliff and $D_2$ is the distance from the farther cliff

$D_1=480m$

Time after which the first echo is heard, $T_1=3s$

Time after which the second echo is heard, $T_2=2s$

Step 2: Calculating the speed of sound

We know that the total distance traveled by the sound will be calculated by adding both the directions, in case of going and coming back, for the nearest cliff.

Thus, the total distance that the sound travels before reaching the person is $2D_1$

Let $v$ be the speed of sound

Speed of sound, $v=\frac{2D_1}{T_1}$
$v=\frac{2\times 480}{3}=320\mathrm{m}/\mathrm{s}$

Hence, the speed of sound is $320m/s$.