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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?


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Solution

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=TotaldistancetraveledabodyTotaltimetime..

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 2×90=180m

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

For 1 step the necessary time is 60120=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

speed=TotaldistancetraveledabodyTotaltimetime=180m0.5sec=360orspeed=360m/s

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


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