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Q.

The figure shows a taut string, initially aligned with the x-axis, which carries a waveform travelling towards the right without any change its shape. The bold line and the dotted line indicate the displacement of the string (i.e., shape of the wave form)at time = t second at time = (t + dt) second, respectively. The speed of particle at point P at t = 2 sec is 1cm/s. Choose the correct statement (s) from the following (assume that dt is positive & slope of y-x at p is 45° )

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a

Particle velocity as a function of position

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b

Particle velocity as a function of position 

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c

Speed of waveform is 1 cm/s and it is moving along negative x-axis

d

Speed of waveform is 1 cm/s and it is moving along positive x-axis

answer is A, C.

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Detailed Solution

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Particle velocity = - wave velocity x slope.

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The figure shows a taut string, initially aligned with the x-axis, which carries a waveform travelling towards the right without any change its shape. The bold line and the dotted line indicate the displacement of the string (i.e., shape of the wave form)at time = t second at time = (t + dt) second, respectively. The speed of particle at point P at t = 2 sec is 1cm/s. Choose the correct statement (s) from the following (assume that dt is positive & slope of y-x at p is 45° )