Question

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

A radio can tune to minimum frequency, \(ν_1 = 7.5 \ MHz= 7.5 × 10^6 Hz \)
Maximum frequency, \(ν_2 = 12\ MHz = 12 × 10^6  Hz \)
Speed of light, \(c = 3 × 10^8 \ m/s \)
Corresponding wavelength for \(ν_1\) can be calculated as:

\(λ_1 = \frac {c}{v_1}\)

\(λ_1 = \frac {3\times 10^8}{7.5\times 10^6 }= 40 \ m\)

Corresponding wavelength for \(ν_2\) can be calculated as:

\(λ_2 = \frac {c}{v_2}\)

\(λ_2 = \frac {3\times 10^8}{12\times 10^6 }= 25 \ m\)

Thus, the wavelength band of the radio is \(40  \ m\) to \(25 \ m\).