Question

8.5 A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?

Answer 1

The corresponding wavelength band is 25 m to 40 m.

Answer 2

The relationship between the speed of light ($c$), frequency ($\nu$), and wavelength ($\lambda$) is given by $c = \nu \lambda$.

Given:

• Frequency band: $7.5$ MHz to $12$ MHz
• Speed of light in vacuum ($c$) = $3 \times 10^8$ m/s

Calculations: For the lower frequency limit ($\nu_1 = 7.5 \text{ MHz} = 7.5 \times 10^6 \text{ Hz}$): $\lambda_1 = \frac{c}{\nu_1} = \frac{3 \times 10^8 \text{ m/s}}{7.5 \times 10^6 \text{ Hz}} = \frac{300}{7.5} \text{ m} = 40 \text{ m}$

For the higher frequency limit ($\nu_2 = 12 \text{ MHz} = 12 \times 10^6 \text{ Hz}$): $\lambda_2 = \frac{c}{\nu_2} = \frac{3 \times 10^8 \text{ m/s}}{12 \times 10^6 \text{ Hz}} = \frac{300}{12} \text{ m} = 25 \text{ m}$