Question

Prove the mathematical value of minimum distance need for echo in water

Answer 1

The minimum distance required for an echo to be produced is 16.6 m. Consider an observer producing a sound at a distance x from a rigid surface. The person hears the first sound as soon as it is produced and next when it travels through a total distance of 2x i.e. (x+x) for approaching the surface and and for returning to the observer.Since the standard speed of sound internationally accepted is 332 m/s and to hear the 2 sounds distinctly i.e., for formation of echo, the minimum speed required is 0.1 second. Accordingly, Speed(S)=Distance(d)/Time(t) or, distance = speed*time or, 2x = 332 m/s * 0.1 s s and s gets cancelled.. or, x = 332 *0.1 m /2 or, x = 33.2 m /2 or, x = 16.6 m
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