Question

A speech signal of $3KHz$ is used to modulate a carrier of frequency $1MHz$, using amplitude modulation, the frequencies of side band will be

Answer 1

Hint:- The side bands of a wave is a band of frequencies that contains power. Side bands are produced during amplitude modulation. The frequencies of these side bands are higher or lower than that of the carrier frequency. In some cases, both the side bands are used to carry the information, while sometimes some portion of the side band is removed.

Complete step-by-step solution :
Step I:
A wave whose amplitude, frequency or phase can be modulated is known as carrier wave. These waves are used for conveying messages or information. The frequency carried by a carrier wave is known as carrier frequency. The frequency of the carrier wave is higher than the input signal.
Step II:
The frequencies of two sidebands- upper sideband and lower sideband are to be calculated.
Given that the frequency of carrier wave ${f_c} = 1MHz$
Converting MHz into KHz
$1MHz = 1000KHz$
${f_c} = 1000KHz$
Frequency of the modulating signal, ${f_m} = 3KHz$
Step III:
Formula used for
Upper side band is written as
$= {f_c} + {f_m}$
$= 1000 + 3$
$= 1003KHz$
Also the formula for lower Side Band is
$= {f_c} - {f_m}$
$= 1000 - 3$
$= 997KHz$
Step IV:
Therefore, frequencies of the side bands are:
Upper side band $= 1003KHz$
Lower Side Band $= 997KHz$
Note:- It is to be noted that when the modulating signal wave is superimposed on a carrier wave having high frequency then sidebands are produced. These side bands are formed from the sum or the difference in frequencies of the modulating wave and the carrier wave. Modulation of waves is done so that the size of the antenna can be reduced and the communication range can be increased.