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At a certain moment, the photograph of a string on which a harmonic wave is travelling to right is shown. Then, which of the following is true regarding the velocities of the points\[P\],\[Q\]and \[R\] on the string.

A. \[{v_p}\]is upwards
B. \[{v_Q} = - {v_R}\]
C. \[\left| {{v_p}} \right| > \left| {{v_Q}} \right| = \left| {{v_R}} \right|\]
D. \[{v_Q} = {v_R}\]

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Last updated date: 16th Jun 2024
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Answer
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Hint: As we know in this photograph if the rope is to go to right direction then \[R\] should go in upward direction and \[P\]should go in downward and \[Q\] should go in upward direction which will help the string to move in right direction and we are saying it by comparing slopes of them.

Complete step by step answer:
In this question we are given three points on a string which has to move in the right direction and a harmonic wave is travelling on string. And we know three points on the string are \[P\],\[Q\]and \[R\].
As we know if the string has to move in right direction then point \[P\] should go in downward direction,
Point \[Q\] should go in upward direction and point \[R\] should go in upward direction which will help the string to move in the right direction as given in question.
\[{v_{po\operatorname{int} }} = - v \times slope\],where \[{v_{po\operatorname{int} }}\]is velocity of any points or particle on string and \[v\] is velocity of string.
And if we talk about speeds of points then points \[Q\] and \[R\] are at the same distance from the y-axis so the velocities of both these will be equal.
And as the slope of \[P\] is greater than Q and R so velocity of \[P\] will be greater than them.
Therefore correct options are C and D.

Note: As we know we have to calculate the velocities of string using the formula but as we are discussing only about directions of movements of particles then we can do it by imagining that on which side the particle should move so that string can go in the right direction.