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## QuestionPhysicsClass 12

A modulating signal is a square wave, as shown in figure,

The carrier wave is given by $$c\left(t\right)=2\sin \left(8\mathit{\pi t}\right)\mathit{volts}$$
$$(i)$$ Sketch the amplitude modulated waveform
$$(\mathit{ii})$$ What is the modulation index?

$$(i)$$ time period of carrier wave, $$T=\frac{2\pi }{8\pi }=0.25s$$ ( $$4$$ oscillation in $$1\mathit{sec}$$ )
from $$0\lt t<0.5$$ , amplitude of modulated wave, $$A=A_M+A_C=1+2=3$$
from $$0.5\lt t<1$$ , amplitude of modulated wave,   $$A=\left(-1\right)+2=1$$

$$(\mathit{ii})$$ Modulation index,   $$\mu =\frac{A_M}{A_C}=\frac 1 2=0.5$$