Question

One of the frequencies used to transmit and receive cellular telephone signals in the United States is 850 MHz. What is the wavelength in meters of these radio waves?

Short answer

The wavelength of these radio waves is 0.353 m or 35.3 cm.

Step-by-step solution

The relation between wavelength and frequency

The relation between the wavelength and frequency of a radiation is as shown below:

\({\bf{C = \nu \times \lambda }}\)

Where, C is the speed of light,\({\bf{\nu }}\)is the frequency and\({\bf{\lambda }}\)is the wavelength of the electromagnetic radiation.

Determination of wave length of the radiation

\(\begin{aligned}{}{\rm{\lambda = c/v}} &\\{\rm{ = (2}}{\rm{.998 \times 1}}{{\rm{0}}^{\rm{8}}}{\rm{m}}{{\rm{s}}^{{\rm{ - 1}}}}{\rm{)/(850 \times 1}}{{\rm{0}}^{\rm{6}}}{{\rm{s}}^{{\rm{ - 1}}}}{\rm{)}}\\{\rm{ = 0}}{\rm{.003527 \times 1}}{{\rm{0}}^{\rm{2}}}{\rm{m}}\\\end{aligned}\)

= 0.353 m or 35.3 cm.