Question

An observer heard his echo $2.5$ seconds after he produced the sound by standing before a wall $400m$ away from him. The speed of the sound in air
$\begin{aligned} & a)320 \\\ & b)160 \\\ & c)330 \\\ & d)200 \\\ \end{aligned}$

Answer 1

The speed of the sound in air can be calculated by dividing the distance travelled by the sound in the air and the time taken by it to travel the given distance. In the case of an echo, the distance travelled by the echo will be twice the distance given because an echo is heard when the sound comes back after hitting a different medium.

Formula used:
$v=\dfrac{s}{t}$

Complete step by step answer:
Let us assume the distance travelled by the sound and time taken by the sound as $s,t$ respectively. Now, the time taken by the sound is given as $2.5$seconds. The distance travelled by the echo will be twice the actual distance as we know an echo travels back and forth before it reaches the observer.
Therefore, the distance is taken as $2s=800m$.
Now, the speed of the sound in air is calculated by dividing the distance and the time taken,
$\begin{aligned} & v=\dfrac{2s}{t} \\\ & v=\dfrac{800}{2.5} \\\ & v=320mps \\\ \end{aligned}$
Therefore, the correct option is option a.

Additional information:
An echo is a sound that is repeated because of reflection. When a rubber ball hits a hard surface, it bounces back. In the same way, a sound wave, when it experiences a smooth or hard object in its direction of motion. In this process, the direction of the sound changes but the echo sounds the same as the originally produced sound.

Note:
Usually, we take the distance travelled by the sound as just as given in the question. The distance given in the question is only the distance between the source and the different medium. For an echo, the distance travelled by the sound is double the actual distance because, after hitting the medium, the sound waves travel in the same but opposite direction.