Question

Am radio signals have frequencies between 550 khz and 1600 khz (kilohertz) and travel with a speed of 3.00 ✕ 108 m/s. what are the wavelengths of these signals?

Answer 1

The minimum frequency is

`f_1 = 550 kHz = 5.50 \cdot 10^5 Hz`
while the maximum frequency is

`f_2 = 1600 kHz = 1.6 \cdot 10^6 Hz`
Using the relationship between frequency f of a wave, wavelength
`\lambda` and the speed of the wave v, we can find what wavelength these frequencies correspond to:

`\lambda_1 = (v)/(f_1)= (3 \cdot 10^8 m/s)/(5.5 \cdot 10^5 Hz)=545 m`

`\lambda_2 = (v)/(f_2)= (3 \cdot 10^8 m/s)/(1.6 \cdot 10^6 Hz)=188 m`

So, the wavelengths of the radio waves of the problem are within the range 188-545 m.