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

Answer:

The given harmonic wave is:

For ,

Where,

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

At

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

Where,

Speed,

Where,

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