Chapter 14, Problem 53A

a.

To determine

Whether speed of the waves in the spring can be changed.

Answer to Problem 53A

No, the speed of waves in the spring cannot be changed.

Explanation of Solution

Introduction:The characteristics of the medium decide the speed of wave in a string. The wavelength and the speed of the waves on the strings determine the frequency of the sound produced.

Speed of wave in a string:

  $\begin{array}{l}v=\sqrt{\frac{T}{\mu }}\\ \mu =\frac{m}{L}\end{array}$

Where, T= tension, $m=$ Mass of string and $l=$ length of string

As the spring is of fixed length, the speed of spring cannot be changed. Since the speed of waves depends on the medium, the wave speed is not changed.

Changes in either the mass per unit length or the tension in the string will produce a different speed. But here the spring is fixed at both ends.

Conclusion:Hence, the speed of waves in the spring cannot be changed.

b.

To determine

The change frequency of the waves in the spring when waves are sent along a spring of fixed length.

Answer to Problem 53A

Yes, the frequency of the wave can be changed.

Explanation of Solution

Introduction:

Frequency can be defined as the number of complete cycles made by source each second. Its SI unit is hertz.

Frequency is the reciprocal of the time period

  $f=\frac{1}{T}$

Where,

  $f$ is the frequency

  $T$ is the time period

Since the frequency is inversely proportional to the time period of the wave in any medium. And depends entirely on the source of the wave. This suggests that if the vibration rate in the spring is increased, time period of oscillation decreased and hence the frequency of the wave increased.

Similarly, if the vibration rate in the spring is decreased, time period of oscillation increased and hence the frequency of the wave decreased.

Conclusion:

The frequency of the wave can be changed.