Question

A radio station utilizes frequencies between commercial AM and FM. What is the frequency of a 11.12-m-wavelength channel?

Short answer

The frequencyof the 11.12 m wavelength channel is 26.98MHz .

Step-by-step solution

Definition of frequency

The number of waves that travel through a particular point in a given amount of time is referred to as frequency.

Given information and Formula to be used

The wavelength of the radiation is $\lambda =11.12m$

The speed of the light is$c=3\times {10}^{8}m/s$

For an electromagnetic wave, the relationship between propagation speed (c), wavelength , and frequency (f) can be expressed as,

$f=\frac{c}{\lambda }$…………….(1)

Calculate the frequency

Using the given data in equation (1), we have

We have

$$\begin{gathered} f=\frac{3\times {10}^{8}m/s}{11.12m} \\ =2.698\times {10}^{8}Hz\left(\frac{1MHz}{{10}^{6}Hz}\right) \\ =26.98MHz \end{gathered}$$

Hence, the frequency is 26.98 MHz.