Question

Draw a diagram of amplitude modulated waves.

Answer 1

Hint: Amplitude of the carrier wave is varied in accordance with the information signal.

Complete step by step answer::
Carrier wave $c(t) = {A_c}\;\sin \;{w_c}t$
Information wave $m(t) = {A_m}\;\sin \;{w_m}t$
Let us take modulated signal $ = \;{C_m}(t) = m(t)$
\[ = {A_c}\sin \;{\omega _c}t + {A_m}\;\sin {\omega _m}t\]
$ = {A_c}[1 + \dfrac{{{A_m}}}{{{A_c}}}\;\sin {\omega _m}t$
$\mu = \dfrac{{{A_m}}}{{{A_c}}} = Modulation\;index$
\[{C_m}(t) = {A_c}\sin \;{\omega _c}t + \mu {A_c}\;\sin {\omega _m}t\sin \;{\omega _c}t\]
The diagram of carrier wave, information signal and amplitude modulation wave is shown below:

Note:
1. $\mu $ is kept $ \leqslant 1$ to avoid distortion.
2. \[{\omega _c} + {\omega _m}\] is called upper side frequency.
3. \[{\omega _c} - {\omega _m}\] is called lower side frequency.