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 $=C_m(t)=m(t)$
$$=A_c\sin {\omega }_{c}t+A_m\sin {\omega }_{m}t$$
$=A_c[1+{\displaystyle \frac{A_m}{A_c}}\sin {\omega }_{m}t$
$\mu ={\displaystyle \frac{A_m}{A_c}}=Modulationindex$
$$C_m(t)=A_c\sin {\omega }_{c}t+\mu A_c\sin {\omega }_{m}t\sin {\omega }_{c}t$$
The diagram of carrier wave, information signal and amplitude modulation wave is shown below:

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