Chapter U5, Problem 21STP

Interpretation Introduction

Interpretation:

The frequency of a radio wave needs to be determined that has a wavelength of $\text{300 m}$.

Concept introduction:

The formula which relates frequency of the light and the wavelength of the light is:

$\nu \text{ = }\frac{\text{c}}{\text{λ}}$

where v is the frequency of the light, c is velocity of light ( ${\text{3×10}}^{\text{8}}\text{ m/sec}$ ), and λ is wavelength of the light.

Answer to Problem 21STP

The frequency of a radio wave is $\text{1000000 Hz}$ that has a wavelength of $\text{300 m}$.

Explanation of Solution

The formula which relates frequency of the light and the wavelength of the light is:

$\nu \text{ = }\frac{\text{c}}{\text{λ}}$ -(1)

where v is the frequency of the light, c is velocity of light ( ${\text{3×10}}^{\text{8}}\text{ m/sec}$ ), and λ is wavelength of the light.

Wavelength of radio wave, $\lambda =300\text{ m}$ (given)

Substituting the values in formula (1):

$\begin{array}{l}\nu \text{ = }\frac{{\text{3×10}}^{\text{8}}\text{ m/sec}}{300\text{ m}}\\ \nu {\text{ = 10}}^6{\text{ sec}}^{-1}\end{array}$

Since, $1\text{ Hz = }\frac{1}{\sec }$ so,

$\nu \text{ = 1000000 Hz}$

Since, the frequency of a radio wave is $\text{1000000 Hz}$ that has a wavelength of $\text{300 m}$ so, the correct option is (c).