Question

The FM radio band in most places goes from frequencies of about 89 MHz to 106 MHz. How long is the wavelength of the radiation at the beginning of the range

Answer 1

2.83 m

Step-by-step explanation:

The relationship between frequency and wavelength for an electromagnetic wave is given by

`\lambda=(c)/(f)`

where

`\lambda` is the wavelength

`c=3.0\cdot 10^8 m/s` is the speed of light

`f` is the frequency

For the FM radio waves in this problem, we have:

`f_1=89 MHz=89\cdot 10^6 Hz` is the minimum frequency, so the maximum wavelength is

`\lambda_2=(c)/(f_1)=(3\cdot 10^8)/(89\cdot 10^6)=3.37 m`

The maximum frequency is instead

`f_2=106 MHz=106\cdot 10^6 Hz`

Therefore, the minimum wavelength is

`\lambda_1=(c)/(f_2)=(3\cdot 10^8)/(106\cdot 10^6)=2.83 m`

So, the wavelength at the beginning of the range is 2.83 m.