Chapter 5, Problem 5.1P

What is the wavelength in meters of an FM radio wave with frequency $v=102.5\text{MHz}$ ?

Interpretation Introduction

Interpretation:

The wavelength in meters of an FM radio wave with a frequency of 102.5 MHz needs to be determined.

Concept introduction:

Electromagnetic radiation can be defined as the waves of the electromagnetic field which can propagate through space and carries the electromagnetic radiant energy.Radio waves, microwaves, infrared, light, ultraviolet, X-rays, and gamma rays are some common example of electromagnetic radiations. The relation between the wavelength and frequency of the electromagnetic radiations is as given below:

$\begin{array}{l}\text{ν = }\frac{\text{c}}{\text{λ}}\\ \text{Here:}\\ \text{ν = frequency}\\ \text{c = speed of light }\\ \text{λ = wavelength}\end{array}$

Answer to Problem 5.1P

The wavelength of given FM radio waves is 2.92 m.

Explanation of Solution

Given information:

Frequency = 102.5 MHz

1 MHz = 10⁶ Hz

Calculation:

Convert MHz to Hz:

$\text{102}\text{.5 MHz ×}\frac{{\text{10}}^{\text{6}}\text{Hz}}{\text{1MHz}}=\text{102}\text{.5 }\times {\text{10}}^{\text{6}}\text{Hz}=\text{102}\text{.5 }\times {\text{10}}^{\text{6}}{\text{ sec}}^1$

Calculate the wavelength for the given frequency:

$\begin{array}{l}\text{ν = }\frac{\text{c}}{\text{λ}}\\ \text{λ = }\frac{\text{3}{\text{.00 ×10}}^{\text{8}}\text{m/sec}}{\text{102}{\text{.5 ×10}}^{\text{6}}{\text{sec}}^{\text{-1}}}\\ \text{λ = 2}\text{.92 m }\end{array}$

Conclusion

Thus, the wavelength of given FM radio waves is 2.92 m.