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Physics

Calculate the minimum distance needed in water to hear the echo.

(Speed of sound in water is 1500 m s-1. Persistence of hearing is 0.1 s.)

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Answer

Given,

  • Speed of sound in water (v) = 1500 m s-1
  • Minimum time to hear an echo (t) = 0.1 s

Let minimum distance to hear an echo be 'd'.

Then,

Speed of sound=2×Minimum distance to hear echo Minimum time to hear an echo=2dt⇒2d=v×t=1500×0.1=150 m⇒d=1502=75 m\text {Speed of sound} = \dfrac {2\times \text {Minimum distance to hear echo}}{\text { Minimum time to hear an echo}} = \dfrac{2\text d}{\text t} \\[1em] \Rightarrow 2\text d = \text v \times \text t = 1500 \times 0.1 = 150\ \text m \\[1em] \Rightarrow \text d = \dfrac{150}{2} = 75\ \text m

So, minimum distance to hear an echo is 75 m.

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