Question

In an amplitude modulation with a modulation index of $0.5$ , the ratio of the carrier wave to that of side band in the modulated wave is
$\begin{align}
  & A.4:1 \\
 & B.1:2 \\
 & C.1:1 \\
 & D.2:1 \\
\end{align}$

Answer 1

Hint: First of all we have to find the formula of the side band in a modulated wave. It is given by the equation,
$side band=\dfrac{\mu {{A}_{C}}}{2}$
Find out the side band of the carrier wave also. Take the ratio of both of them. This will give the required answer for the question.

Complete step-by-step answer:
 First of all let us write the terms mentioned in the question and their values.
The modulation index of the wave in the amplitude modulation is given as,
$\mu =0.5$
The side band in a modulated wave is given by the equation,
$side band=\dfrac{\mu {{A}_{C}}}{2}$
Where $\mu $ be the modulation index and ${{A}_{C}}$ be the side band in the carrier wave.
The side band in the carrier wave is given by the equation,
$sideband={{A}_{C}}$
Taking the ratio on both the side band will give,
$\dfrac{{{A}_{C}}}{\dfrac{\mu {{A}_{C}}}{2}}=ratio$
We can take the $2$ in to the numerator so that the equation becomes,
$\dfrac{2{{A}_{C}}}{\mu {{A}_{C}}}=ratio$
Cancel the common terms in it will give,
$\dfrac{2}{\mu }=ratio$
Substituting the value of modulation index in this equation will give,
$\dfrac{2}{0.5}=ratio$
That is we can say that the ratio between carrier wave and amplitude wave is,
$ratio=4:1$
Therefore the answer for the question is obtained. The correct answer is option A.

Note: Amplitude modulation is defined as a way of modulating a wave in order to transmit messages with the help of a carrier wave commonly. In an amplitude modulation, the amplitude of the signal strength of the carrier wave is changed which is proportional to that of the message signal, such as an audio signal. Currently, this is widely used in electronic communication. This process is used in portable two-way radios, citizens band radio, and VHF aircraft radio and in modems for computers.