Question

1. An FM radio station broadcasts at a frequency of 101.3 MHz . What is the wavelength?
2. What is the frequency of a sound source that produces the same wavelength in 20⁰C air?

Short answer

Part (a) The wavelength of the FM radio wave is 2.96 m.

Part (b) The frequency of a sound source that produces the same wavelength in 20⁰ C is 115.8 Hz.

Step-by-step solution

Part (a) Step 1. Given information

The frequency of the FM radio signal is $f=101.3\times {10}^{6}Hz$

The speed of any electromagnetic wave is $c=3\times {10}^{8}m/s$

The speed of sound in 20⁰C air is$v=343m/s$

Part (a) Step 2. Calculating the wavelength of the radio FM signal:

Wavelength is defined as the distance between consecutive crests or troughs.

The formula to calculate the wavelength in terms of wave speed is given by

$\lambda =\frac{c}{f}$

Substitute $3\times {10}^{8}m/s$for c and $101.3\times {10}^{6}Hz$for f into the above formula to calculate the wavelength.

$$\begin{gathered} \lambda =\frac{3\times {10}^{8}m/s}{101.3\times {10}^{6}Hz} \\ =2.96m \end{gathered}$$

Part (b) Step 1. Calculate the frequency of the sound source:

Frequency is defined as the number of complete waves or oscillations travelling in unit time.

The formula to calculate the frequency in a periodic wave is given as:

$f_s=\frac{v}{\lambda }$

Substitute 343 m/s for v, 2.96 m for $\lambda$into the above formula to calculate the frequency.

$$\begin{gathered} f_s=\frac{343m/s}{2.96m} \\ =115.8Hz \end{gathered}$$