Question

In amplitude modulation, the bandwidth is:
A. Equal to the signal frequency
B. Twice the signal frequency
C. Thrice the signal frequency
D. Four times the signal frequency

Answer 1

Hint:- In this question, we can find the lower sides and upper side frequency of carrier and modulated signals. After that, we can calculate the bandwidth in the amplitude modulation.

Complete step-by-step solution :
We know that ${\omega _c}$ is the frequency of carrier signal and ${\omega _m}$ is the frequency of modulated frequency.
Then the lower side frequency of amplitude modulated wave is given as:
$\dfrac{{{\omega _c} - {\omega _m}}}{2}$
And the upper side frequency of amplitude modulated wave is given as:
$\dfrac{{{\omega _c} + {\omega _m}}}{2}$
We know that the signal frequency which is present in the side bands is given as= $\dfrac{{{\omega _m}}}{2}$
Again, we know that the bandwidth of the amplitude modulation is given as difference between the upper side frequency of the amplitude modulated wave and lower side frequency of the amplitude modulated wave. So,
$\dfrac{{{\omega _c} + {\omega _m}}}{2} - \dfrac{{{\omega _c} - {\omega _m}}}{2} = \dfrac{{{\omega _c} + {\omega _m} - {\omega _c} + {\omega _m}}}{2}$
Bandwidth$= 2\dfrac{{{\omega _m}}}{2}$
Which is twice the signal frequency. Hence, in amplitude modulation, the bandwidth is twice the signal frequency. Therefore, option B is correct.

Additional Information: - We know that when a carrier signal is modulated then some signals are created on the sides of the steady signals. These sidebands of the signals carry the actual modulation of the amplitude. These sidebands are generated above and below the main carrier signal.
The process of modulation is the same as the mixing of two signals and as a result both sum and difference of frequencies are produced. The process of modulation has the same concept as the concept of interference in light waves.

Note:- We have to remember the formula of the lower side frequency and upper side frequency to find the bandwidth. We have to calculate the answer in a way that it will be in the multiples of signal frequency.