Chapter 17, Problem 108A

Interpretation Introduction

Interpretation: The wavelength of a radio wave whose frequency is given is to be calculated.

Concept introduction: The wavelength and frequency of a wave are inversely related which means if the wavelength of the wave increases, the frequency of the wave decreases and vice versa.

The formula used is:

  $\lambda =\frac{c}{\nu }$

where

  $\lambda$ = wavelength of the wave

  $c$ = speed of light = $3\times {10}^8{\text{ms}}^{\text{-1}}$

  $\nu$ = frequency of the wave

Answer to Problem 108A

The wavelength of the radio wave with frequency $93.1\times {10}^6{\text{s}}^{\text{-1}}$ is $3.22\text{m}$

Explanation of Solution

It is given that the frequency of the radio wave is $93.1\times {10}^6{\text{s}}^{\text{-1}}$

Putting in the values we get

  $\begin{array}{l}\lambda =\frac{3\times {10}^8{\text{ms}}^{\text{-1}}}{93.1\times {10}^6{s}^{\text{-1}}}\\ \lambda =3.22\text{m}\end{array}$