Question

TV and radio stations transmit in specific frequency bands of the radio region of the electromagnetic spectrum.
(a) TV channels 2 to 13 (VHF) broadcast signals between the frequencies of 59.5 and 215.8 MHz, whereas FM radio stations broadcast signals with wavelengths between 2.78 and 3.41 m. Do these bands of signals overlap?
(b) AM radio signals have frequencies between 550 and 1600 kHz. Which has a broader transmission band, AM or FM?

Answer 1

Answer:

a) Yes, these bands of signals overlap.

b) FM has broader transmission band.

Explanation:

a) Frequency range of TV channels = 59.5 to 215.8 MHz

Wavelength range of FM radio = 2.78 m to 3.41 m

Frequency of the wave = $\nu$

Wavelength of the wave = $\lambda$

Speed of light = c = $3\times 10^8 m/s$

$\nu =\frac{c}{\lambda }$

Frequency of wave with, $\lambda = 2.78 m$

$\nu =\frac{3\times 10^8 m/s}{2.78 m}=1.079\times 10^8 Hz$

$1.079\times 10^8 Hz=1.079\times 10^8\times 10^{-6} MHz=107.9 MHz$

Frequency of wave with, $\lambda = 3.41m$

$\nu =\frac{3\times 10^8 m/s}{3.41 m}=8.798\times 10^7 Hz$

$8.798\times 10^7 Hz=8.798\times 10^7\times 10^{-6} MHz=87.98 MHz$

Frequency range of FM = 87.89 to 107.9 MHz

Frequency range of TV channels = 59.5 to 215.8 MHz

Yes, these bands of signals overlap.

b)  

Frequency range of AM = 550 to 1600 kHz

1 kHz = 0.001 MHz

550 to 1600 kHz = $550\times 0.001 MHz$ to $1600\times 0.001 MHz$

= 0.55 MHz to 1.6 MHz

Frequency range of AM = 0.55 to 1.6 MHz

Frequency range of FM = 87.89 to 107.9 MHz

FM has broader transmission band.