Question

A soldier walks forwards a high wall taking $120$ steps per minute. When he is at a distance of $90m$ from the wall he observes that the echo of the step coincides with the next step. The speed of sound must be?

Answer 1

Given data

1. The number of steps by the boy is $120steps.$
2. The total time taken for a walk is $60seconds.$
3. Distance travel by the boy is $90m$.

Formulae

1. We know, that speed is the time rate of change in distance, i.e, $speed=\frac{Totaldis\tan cetraveledabody}{Totaltimetime}.$.

Finding the speed of the sound wave

It is clear that the total distance traveled by the sound wave produced by the soldier's step after reflected from the wall is $2\times 90=180m$

Now, the necessary time for $120$steps in $60$ seconds.

For 1 step the necessary time is $\frac{60}{120}=0.5seconds.$

From the question, the echo of the step coincides with the next step. So, the time interval between two echoes is $0.5seconds.$

So, the speed of the sound is

$$\begin{gathered} speed=\frac{Totaldis\tan cetraveledabody}{Totaltimetime}=\frac{180m}{0.5sec}=360 \\ orspeed=360m/s \end{gathered}$$

Therefore, the speed of sound is $360m/s.$