Calculating Wavelengths of Radio Waves

Calculate the wavelengths of a 1530-kHz AM radio signal, a 105.1-MHz FM radio signal, and a 1.90-GHz cell phone signal.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
The relationship between wavelength and frequency is $c = fλ$ , where $c = 3 . 00 \times 10^{8} m / s$ is the speed of light (the speed of light is only very slightly smaller in air than it is in a vacuum). We can rearrange this equation to find the wavelength for all three frequencies.
Solution
Rearranging gives

$λ = \frac{c}{f} .$
24.7

(a) For the $f = 1530 kHz$ AM radio signal, then,

$\begin{array}{l} λ & = & \frac{3.00 \times 10^{8} m/s}{1530 \times 10^{3} cycles/s} \\ = & 196 m. \end{array}$
24.8

(b) For the $f = 105.1 MHz$ FM radio signal,
$\begin{array}{l} λ & = & \frac{3.00 \times 10^{8} m/s}{105.1 \times 10^{6} cycles/s} \\ = & 2.85 m. \end{array}$
24.9

(c) And for the $f = 1.90 GHz$ cell phone,
$\begin{array}{l} λ & = & \frac{3 . 00 \times 10^{8} m/s}{1.90 \times 10^{9} cycles/s} \\ = & 0.158 m. \end{array}$
24.10
Discussion
These wavelengths are consistent with the spectrum in Figure 24.9. The wavelengths are also related to other properties of these electromagnetic waves, as we shall see.

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