Chapter 13, Problem 1OQ

To determine

The condition which is not mandatory for mechanical waves.

Answer to Problem 1OQ

Option (b).

Explanation of Solution

All mechanical waves are the result of some kind of disturbance at a point in a medium. Waves carry energy. A wave is characterized by its wavelength, frequency, and speed. Ripples in water, sound waves etc. are some of the examples for mechanical waves.

Write the relation between frequency and wavelength of a mechanical wave.

    $v=f\lambda$

Here, $v$ is the speed of wave, $f$ is the frequency of wave, and $\lambda$ is the wavelength.

Write the equation for speed of wave through a stretched string.

    $v=\sqrt{\frac{T}{\mu }}$

Here, $T$ is the tension on the string, $v$ is the speed of wave, and $\mu$ is the linear mass density of string.

Conclusion:

A wave can have any shape. A wave of single frequency can be sinusoidal. If there exist multiple frequencies in a wave, shape will not be sinusoidal. Thus, option (b) is correct.

Some kind of disturbance is a mandatory condition for the generation of mechanical waves. For example, ripple in water is result of stone dropped in water. Thus, option (a) is incorrect.

All kind of mechanical waves possess energy. If no energy, it cannot propagate. Thus, option (c) is incorrect.

All mechanical waves require a medium to propagate. The reason why sound is not heard in moon is that it has no any medium for propagation. Thus, option (d) is incorrect.

From the above expression for $v$, it is seen that speed depends on linear density of string. If the medium is a solid or gas, it will depend on modulus of elasticity and the density of medium. Thus, option (e) is incorrect.