Question

a. An FM radio station broadcasts at a frequency of 101.3 MHz. What is the wavelength?

b. What is the frequency of a sound source that produces the same wavelength in 20°C air?

Answer 1

(a)

Use the following formula to calculate the wavelength of the signal.

\(\lambda=\frac{c}{f}\)

Here, \(\lambda\) is the wavelength, \(f\) is the frequency, and \(c\) is the speed of light.

Substitute \(3 \times 10^{8} \mathrm{~m} / \mathrm{s}\) for \(c, 101.3 \mathrm{MHz}\) for \(f\) in the above equation.

$$ \begin{aligned} \lambda &=\frac{3 \times 10^{8} \mathrm{~m} / \mathrm{s}}{101.3 \mathrm{MHz}\left(\frac{10^{6} \mathrm{~Hz}}{1 \mathrm{MHz}}\right)} \\ &=2.96 \mathrm{~m} \end{aligned} $$

Hence, the wavelength of the signal is \(2.96 \mathrm{~m}\)

 

(b)

The speed \((v)\) of sound in air at \(20^{\circ} \mathrm{C}\) is \(343 \mathrm{~m} / \mathrm{s}\).

Use the following formula to calculate the frequency of sound source.

\(f=\frac{v}{\lambda}\)

Substitute \(343 \mathrm{~m} / \mathrm{s}\) for \(v\) and \(2.96 \mathrm{~m}\) for \(\lambda\)

\(f=\frac{343 \mathrm{~m} / \mathrm{s}}{2.96 \mathrm{~m}}\)

\(=116 \mathrm{~Hz}\)

Hence, the frequency of the sound source is \(116 \mathrm{~Hz}\).