Question

Voltage of modulating wave of 5V with 10 MHz frequency was superimposed on carrier wave of frequency 20 MHz and voltage 20V then the modulation index is
A. 0.25
B. 1.25
C. 2.43
D. 64.0

Answer 1

We are given the frequency and voltage of a modulating wave and a carrier wave. It is said that the modulating wave was superimposed on the carrier wave. We are asked to find the modulation index of the superimposed wave. We have an equation relating modulation index and voltage of carrier and modulating wave. By substituting the values we will get the required solution.

Formula used:
$m=\dfrac{{{V}_{m}}}{{{V}_{c}}}$

Complete step-by-step answer:
In the question we are given the frequency and voltage of a modulating wave.
Let ‘${{V}_{m}}$’ be the voltage of the modulating wave. Then,
${{V}_{m}}=5V$
Let ‘${{f}_{m}}$’ be the frequency of the modulating wave. Then,
${{f}_{m}}=10MHz$
It is said that this wave was superimposed on a carrier wave, and the frequency and voltage of the carrier wave is also given.
Let ‘${{V}_{c}}$’ and ‘${{f}_{c}}$’ be the voltage and frequency of the carrier wave respectively. Then we have,
${{V}_{c}}=20V$
${{f}_{c}}=20MHz$
We know that the modulation index of a wave is the ratio of voltage of modulated wave and voltage of carrier wave, i.e.
$m=\dfrac{{{V}_{m}}}{{{V}_{c}}}$
We can substitute the known values in the above equation. Thus we get,
$\Rightarrow m=\dfrac{5}{20}$
$\Rightarrow 0.25$
Therefore we get the modulation index of the signal as 0.25.

So, the correct answer is “Option A”.

Note: When we modulate a carrier wave using a modulating wave we alter the phase, amplitude or frequency of the carrier wave.
Depending on the alterations made modulation is of three types; phase modulation, amplitude modulation and frequency modulation.
Modulation index is simply the level of modulation that a carrier wave undergoes.