NCERT Class 11 Physics Solutions: Chapter 15 – Waves-Part 12

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Question 15.22:

A travelling harmonic wave on a string is described by

What are the displacement and velocity of oscillation of a point at ? Is this velocity equal to the velocity of wave propagation?

Locate the points of the string which have the same transverse displacements and velocity as the point at


The given harmonic wave is:

For ,


The velocity of the oscillation at a given point and time is given as:


Now, the equation of a propagating wave is given by:




Hence, the velocity of the wave oscillation at s is not equal to the velocity of the wave propagation.

Propagation constant is related to wavelength as:

Therefore, all the points at distances , i.e. and so on for will have the same displacement as the points at