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Question

A transverse wave is propagating through a medium. The potential energy associated with vibrating particle is maximum when the displacement of the particle from the mean position is

A
Zero
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B
half of the amplitude
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C
equal to the amplitude
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D
none of the above
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Solution

The correct option is C equal to the amplitude
We know that at mean position, velocity of particle is maximum.
Hence kinetic energy associated with particle will be maximum at mean position.
Similarly,
vP=0 at the extreme position, where displacement of particle is equal to amplitude.
i.e y=±A
Now the total energy of particle is,
P.E+K.E=T.E
P.E of vibrating particle will be maximum at extreme position, where K.E is minimum.
option (c) is correct.

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