Chapter 14.2, Problem 23PP

To determine

Change in wavelength of wave when the period is reduced by one half.

Explanation of Solution

Introduction:

Period is defined as the time needed for one total wave to pass. So, period will not rise if wavelength rises.

The wavelength is the distance between successive waves and the period is the time taken by waves to cover that distance.

The relation of wavelength and period is described below:

  $vT=\lambda$

Where,

  $\lambda$ is the wavelength, T is the period and v is the speed.

Period is defined as the time needed for one total wave to pass. Wavelength and period are directly related to each other. So, period will rise if wavelength rises. This means reduced one-half the period of wave reduces one-half the frequency of wave.

Conclusion:

Hence, reducing one-half the period of wave will reduce the same one half of the wavelength of its original value.