Sound WavesHard

Question

A stone thrown into still water, creates a circular wave pattern moving radially out wards. If r is the distance measured from the center of the pattern.the amplitude of the wave arises as :

Options

A.r-1/2
B.r-1
C.r-2
D.r-3/2

Solution

     
             
Energy of crest (P.E) = (2πr. dr × h × ρ) × g × h
Now, as crest spread, this energy Eremain contant. So,
2π rdrh2 ρg = E
⇒     h = or h ∝ r-1/2

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