Chapter 25, Problem 7A

Distinguish between the period and the frequency of a vibration or a wave. How do they relate to one another?

To determine

To distinguish: the period and frequency of a wave.

Also to express the relationship between them.

Explanation of Solution

Given Information:

The terms frequency and period of a wave

Vibrations or wave exhibit a periodic repetition of itself after a finite time. This time period over which the wave covers one full cycle of motion and then repeats the same pattern is called as fundamental period or period of a wave. This is denoted as T. Now, the number of cycles traversed by the wave in one second is termed as frequency of the wave. It is denoted by f.

This can be explained in the case of a simple pendulum as an example.

Consider the pendulum motion shown below. Here, the fundamental period or period, T is the duration for completing one full cycle of back and forth motion. This represents the movement of the pendulum bob from center to one extreme point and then to the other extreme point through the center as shown in the figure.

  

Now, the term frequency f of a wave is defined as the number of cycles completed in one second.

The parameters period and frequency of a wave are inversely related to each other. The mathematical relationship between them is given by,

  $f=\frac{1}{T}$