NCERT Class 11 Physics Solutions: Chapter 15 – Waves-Part 6

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Question 15.11:

The transverse displacement of a string (clamped at its both ends) is given by

Where are in The length of the string is and its mass is

Answer the following:

Does the function represent a travelling wave or a stationary wave?

Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave?

Determine the tension in the string.

Answer:

sine wave in opposite direction is showing in figure.

Figure Shown the Sine Wave in Opposite Direction

Loading Image

The general equation representing a stationary wave is given by the displacement function:

This equation is similar to the given equation:

Hence, the given function represents a stationary wave.

A wave travelling along the positive x-direction is given as:

The wave travelling along the negative direction is given as:

The superposition of these two waves yields:

The transverse displacement of the string is given as:

Comparing equations we have:

Wavelanght

It is given that:

Frequency,

Wave speed,

The velocity of a transverse wave travelling in a string is given by the relation:

Where,

Velocity of the transverse wave,

Mass of the string,

Length of the string,

Mass per unit length of the string,

Tension in the string

From equation tension can be obtained as: