A radio can tune in to any station in the 7.5 MHz to 12 MHz band.

Question:

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

Solution:

A radio can tune to minimum frequency, ν1 = 7.5 MHz= 7.5 × 106 Hz

Maximum frequency, ν2 = 12 MHz = 12 × 106 Hz

Speed of light, c = 3 × 108 m/s

Corresponding wavelength for ν1 can be calculated as:

$\lambda_{1}=\frac{c}{v_{1}}$

$=\frac{3 \times 10^{8}}{7.5 \times 10^{6}}=40 \mathrm{~m}$

Corresponding wavelength for ν2 can be calculated as:

$\lambda_{2}=\frac{c}{v_{2}}$

$=\frac{3 \times 10^{8}}{12 \times 10^{6}}=25 \mathrm{~m}$

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

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