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Radio Max broadcasts on a frequency of [tex]$99.7 \times 10^6 \text{ Hz}$[/tex]. Calculate the wavelength of the radio waves.

Answer :

We start with the formula that relates the speed of light, frequency, and wavelength:

[tex]$$
\lambda = \frac{c}{f}
$$[/tex]

where
- [tex]$\lambda$[/tex] is the wavelength (in meters),
- [tex]$c$[/tex] is the speed of light ([tex]$3 \times 10^8 \, \text{m/s}$[/tex]),
- [tex]$f$[/tex] is the frequency (in Hz).

Given the frequency is

[tex]$$
f = 99.7 \times 10^6 \, \text{Hz},
$$[/tex]

we substitute the known values into the formula:

[tex]$$
\lambda = \frac{3 \times 10^8 \, \text{m/s}}{99.7 \times 10^6 \, \text{Hz}}.
$$[/tex]

To simplify the calculation, first notice that

[tex]$$
\frac{3 \times 10^8}{99.7 \times 10^6} = \frac{3}{99.7} \times \frac{10^8}{10^6} = \frac{3}{99.7} \times 10^2.
$$[/tex]

Calculating the fraction [tex]$\frac{3}{99.7}$[/tex] gives approximately [tex]$0.03009$[/tex]. Multiplying by [tex]$10^2$[/tex] (or 100):

[tex]$$
\lambda \approx 0.03009 \times 100 = 3.009 \, \text{meters}.
$$[/tex]

Thus, the wavelength of the radio waves is approximately

[tex]$$
3.009 \, \text{meters}.
$$[/tex]

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