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](https://tex.z-dn.net/?f=%5Cnu%20)
Wavelength of the wave = ![\lambda](https://tex.z-dn.net/?f=%5Clambda%20)
Speed of light = c = ![3\times 10^8 m/s](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E8%20m%2Fs)
![\nu =\frac{c}{\lambda }](https://tex.z-dn.net/?f=%5Cnu%20%3D%5Cfrac%7Bc%7D%7B%5Clambda%20%7D)
Frequency of wave with, ![\lambda = 2.78 m](https://tex.z-dn.net/?f=%5Clambda%20%3D%202.78%20m)
![\nu =\frac{3\times 10^8 m/s}{2.78 m}=1.079\times 10^8 Hz](https://tex.z-dn.net/?f=%5Cnu%20%3D%5Cfrac%7B3%5Ctimes%2010%5E8%20m%2Fs%7D%7B2.78%20m%7D%3D1.079%5Ctimes%2010%5E8%20Hz)
![1.079\times 10^8 Hz=1.079\times 10^8\times 10^{-6} MHz=107.9 MHz](https://tex.z-dn.net/?f=1.079%5Ctimes%2010%5E8%20Hz%3D1.079%5Ctimes%2010%5E8%5Ctimes%2010%5E%7B-6%7D%20MHz%3D107.9%20MHz)
Frequency of wave with, ![\lambda = 3.41m](https://tex.z-dn.net/?f=%5Clambda%20%3D%203.41m)
![\nu =\frac{3\times 10^8 m/s}{3.41 m}=8.798\times 10^7 Hz](https://tex.z-dn.net/?f=%5Cnu%20%3D%5Cfrac%7B3%5Ctimes%2010%5E8%20m%2Fs%7D%7B3.41%20m%7D%3D8.798%5Ctimes%2010%5E7%20Hz)
![8.798\times 10^7 Hz=8.798\times 10^7\times 10^{-6} MHz=87.98 MHz](https://tex.z-dn.net/?f=8.798%5Ctimes%2010%5E7%20Hz%3D8.798%5Ctimes%2010%5E7%5Ctimes%2010%5E%7B-6%7D%20MHz%3D87.98%20MHz)
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 =
to ![1600\times 0.001 MHz](https://tex.z-dn.net/?f=1600%5Ctimes%200.001%20MHz)
= 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.