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Question

A stone is dropped into a well in which the level of water is h below the top of the well. If v is speed of sound in the air, the time T after which the splash is heard is given by

A
T=2hv
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B
T=2hg+hv
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C
T=2hg+h2v
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D
T=h2g+2hv
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Solution

The correct option is B T=2hg+hv
Total time taken to hear the sound of splash = Time taken by stone to reach the water surface inside the well + Time taken by sound of splash to reach the ear through air.

Let t1 be time taken by the stone to reach the water surface
h=ut1+12gt21
As stone is dropped, so, u=0
h=12gt21
t1=2hg.......(i)

Also, time taken t2 by sound of splash to reach the ear through air is
t2=hv..........(ii)
Total time taken to hear the sound of splash T=t1+t2=2hg+hv

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