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Question

A transverse sinusoidal wave moves along a string in the positive xdirection at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snapshot of the wave is shown in the figure. The velocity of a particle at P when its displacement is 5 cm along yaxis is


A
3π50^j m/s
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B
3π50^j m/s
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C
3π50^i m/s
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D
3π50^i m/s
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Solution

The correct option is A 3π50^j m/s
Angular frequency of the wave,
ω=vk=2πvλ=2π×0.10.5
ω=2π5 rad/s
So, speed of particle at P when its displacement is 5 cm along y axis is
vp=ωA2y2=2π511001400
vp=3π50 m/s
It is shown in the figure that particle is going in +y axis direction, so velocity is vp=3π50 ^j m/s

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