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 $25 \ m$.