Question

FM radio goes from 88 to 108 Mz.  AM goes from 535 to 1605 kHz.   What wavelengths do these imply?

Answer 1

(A) Range of frequencies for \(F M\) radio \(88 \mathrm{~Hz}-108 \mathrm{MHz}\)

Hence, for the lower frequency the corresponding wavelength is

\(\lambda=\frac{c}{f}\)

Or, \(\lambda=\frac{3 \times 10^{8}}{88 \times 10^{6}} m\)

\(\lambda=3.4 m\)

And for the higher frequency, the corresponding wavelength is \(\lambda=\frac{c}{f}\)

Or, \(\lambda=\frac{3 \times 10^{8}}{108 \times 10^{6}} m\)

\(\lambda=2.78 m\)

Hence the range of wavelength for FM Radio is \(2.78 \mathrm{~m}\) to \(3.4 \mathrm{~m}\)

(B) Range of frequencies for \(\mathrm{AM}\) radio is \(535 \mathrm{kHz}-1700 \mathrm{kHz}\)

Hence, for the lower frequency, the corresponding wave length is

\(\lambda=\frac{\mathrm{c}}{\mathrm{f}}\)

\(\lambda=\frac{3 \times 10^{8}}{535 \times 10^{3}} m\)

\(\lambda=560.7 \mathrm{~m}\)

And for the higher frequency the corresponding wavelength is

\(\lambda=\frac{c}{f}\)

\(\lambda=\frac{3 \times 10^{8}}{1605 \times 10^{3}} m\)

\(\lambda=186.9 \mathrm{~m}\)

Hence, the range of wavelength for AM radio is \(186.9 m-560.7 m\)