Question

The frequency deviation in a FM transmission is 18.75 kHz. If it broadcasts in 88- 108 MHz band, then the percentage modulation is
(A) 10%
(B) 25%
(C) 50%
(D) 75%

Answer 1

Hint :The broadcast of the frequency band 88- 108 MHz is FM radio and its maximum modulating frequency is 75 kHz. Frequency is the characteristic of the source and thus during propagation it does not change. Modulation is the process of converting data into radio waves by adding information to an electronic or optical carrier signal
The percentage of modulation is given as: ${\mu }_f={\displaystyle \frac{\mathrm{\Delta }{f}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}}}{\mathrm{\Delta }{f}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}$ where $\mathrm{\Delta }{f}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}}$ is actual modulating frequency and $\mathrm{\Delta }{f}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is maximum modulating frequency.

Complete Step By Step Answer:
From the question, we know that the frequency deviation in a FM transmission is $\delta =18.75\mathrm{k}\mathrm{H}\mathrm{z}$ .
We know that the nature of broadcast of the given frequency band 88- 108 MHz is FM radio.
The commercial FM broadcasting uses a maximum modulating frequency of 75 kHz and minimum modulating frequency of 15 kHz.
The percentage of modulation is equal to the ratio of actual modulating frequency to the maximum modulating frequency.
 ${\mu }_f={\displaystyle \frac{\mathrm{\Delta }{f}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}}}{\mathrm{\Delta }{f}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}$
Substitute the given values in the above expression, we get,
 $$\begin{gathered} {\mu }_f={\displaystyle \frac{18.75}{75}}\times 100 \\ =25\mathrm{\%} \end{gathered}$$
Thus, the percentage of modulation is 25% and option (B) is correct.

Note :
Frequency modulation (FM) is the process of changing the frequency of the carrier voltage in accordance with the instantaneous value of the modulating signal. The original frequency of the carrier signal is called resting frequency or centre frequency and it is the allotted frequency of the transmitter.
When the audio signal is applied, the carrier frequency changes and the quantity by which the frequency of the carrier wave shifts above or below the centre frequency is termed as frequency deviation.