Chapter U5.115, Problem 6E

Interpretation Introduction

Interpretation:

The wavelength of a radio station needs to be determined that broadcasts at a frequency of $\text{790 MHz (7}\text{.9}\times {\text{10}}^8{\text{ s}}^{\text{-1}})$.

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 6E

The wavelength of a radio station that broadcasts at a frequency of $\text{790 MHz (7}\text{.9}\times {\text{10}}^8{\text{ s}}^{\text{-1}})$ is $\text{0}\text{.38 m}$.

Explanation of Solution

Rearranging the formula (1) as:

$\text{λ = }\frac{\text{c}}{\nu }$ - (2)

Frequency, $\nu \text{ = 790 MHz (7}\text{.9}\times {\text{10}}^8{\text{ s}}^{\text{-1}})$ (given)

Substituting the values in formula (2):

$\begin{array}{l}\nu \text{ = }\frac{{\text{3×10}}^{\text{8}}\text{ m/sec}}{\text{7}\text{.9}\times {\text{10}}^8{\text{ s}}^{\text{-1}}}\\ \nu \text{ = 0}\text{.38 m}\end{array}$

Hence, the wavelength of a radio station that broadcasts at a frequency of $\text{790 MHz (7}\text{.9}\times {\text{10}}^8{\text{ s}}^{\text{-1}})$ is $\text{0}\text{.38 m}$.