A radio station transmits on 97.4 MHz - Edexcel - GCSE Physics Combined Science - Question 3 - 2020 - Paper 1

To find the length of the aerial, we first need to calculate the wavelength (λ) of the radio waves using the formula:

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

Where:

• $v = 3.00 \times 10^8 \text{ m/s}$ (the speed of the radio waves)
• $f = 97.4 \text{ MHz} = 97.4 \times 10^6 \text{ Hz}$ (the frequency of the radio waves)

Substituting the values into the formula, we get:

$\lambda = \frac{3.00 \times 10^8}{97.4 \times 10^6}$

Evaluating this results in:

$\lambda \approx 3.08 \text{ m}$

Since the length of the aerial must be half of the wavelength:

$\text{Length of aerial} = \frac{\lambda}{2} \approx \frac{3.08}{2} \approx 1.54 \text{ m}$