Question

The audio signal having a frequency 500 Hz and voltage 2.6V, shows a deviation of 5.2KHz in a Frequency Modulation system. If the audio signal voltage changes to 8.6V, then calculate the new deviation obtained.
A. 17.2KHz
B. 19.6KHz
C. 25.6KHz
D. 14.6KHz

Answer 1

Hint:Before we start addressing the problem, we need to know about what data has been provided and what we need to solve. Here they have given the audio signal frequency, its voltage, and the deviation in the frequency modulation system. So, if the signal of the voltage changes by some value, then, we need to calculate the new deviation of an audio signal. For this first, we need to calculate the frequency deviation constant and then we get the new deviation as follows.

Formula Used:
The formula to find the deviation in FM wave is given by,
\[\Delta f = {K_f}{A_m}\]……… (1)
Where, \[{K_f}\] is frequency deviation constant and \[{A_m}\] is amplitude (voltage) of modulating signal.

Complete step by step solution:
To find when the deviation in FM wave we have,
\[\Delta f = {K_f}{A_m}\]
By rearranging the above equation for \[{K_f}\]we get,
\[{K_f} = \dfrac{{\Delta f}}{{{A_m}}}\]
Now, substitute the value of \[\Delta f = 5.2KHz\] and \[{A_m} = 2.6V\] in the above equation
\[{K_f} = \dfrac{{5.2}}{{2.6}}\]
\[\Rightarrow {K_f} = 2\]

Now, we need to find the new deviation obtained when the voltage changes, i.e., \[{A_m} = 8.6V\]. The new frequency deviation is given by,
\[\Delta f = {K_f}{A_m}\]
Here we know the value of \[{K_f}\] and \[{A_m}\].
So, substitute these in above equations we get,
\[\Delta f = {K_f}{A_m}\]
\[\Rightarrow \Delta f = 2 \times 8.6\]
\[\therefore \Delta f = 17.2KHz\]
Therefore, the new frequency deviation is 17.2KHz.

Hence, option A is the correct answer.

Note: Frequency modulation is used to reduce the noise and thereby improve the quality of radio reception. It consumes less power than amplitude modulation. When there is modulation, we generally need to properly demodulate it while still recovering the original signal. FM demodulators, also known as FM discriminators or FM detectors, are used in such instances.