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Question

For the yx graph of a transverse wave in a string is as shown in figure. Which of the following options is correct ?


A
kinetic energy of the particle is maximum at point A
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B
kinetic energy of the particle is maximum at point B
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C
kinetic energy of the particle is minimum at point B
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D
kinetic energy of the particle is minimum at point C
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Solution

The correct option is B kinetic energy of the particle is maximum at point B
From the given yx graph , we can deduce that ,
yA>yC>yBy2A>y2C>y2B

Multiplying with 1 we get

(y2A)<(y2C)<(y2B)

Adding square of amplitude A2 we get

(A2y2A)<(A2y2C)<(A2y2B) ..........(1)

We know that , Kinetic energy of a particle executing SHM about y=0 is given by

K=12mω2(A2y2) .......(2)

From (1) and (2) we get, KA<KC<KB
Therefore, kinetic energy is maximum at point B.
Thus, option (b) is the correct answer.

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