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Question

An amplitude-modulated wave is represented by, Cm=10(1+0.2sin12560t)sin(1.11×104t)V, the modulating frequency in kHz will be


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Solution

Step 1. Given data:

An amplitude-modulated wave =Cm=10(1+0.2sin12560t)sin(1.11×104t)V..........1

Step 2. Formula used:

In general,

An amplitude-modulated wave =Cm=Ac(1+AmAcsinωmt)sinωctV..........2

where, Amis the Amplitude of modulating wave in m

Acis the Amplitude of carrier wave in m

sinωmtand sinωct is the phase of modulating wave and carrier wave respectively.

Step 3. Find the modulating frequency:

By comparing equations 1and 2, we get

ωm=12560rad/sec

fm=ωm2πHz{ωm=2πfm}

where, fm is the frequency of modulation

fm=125602×3.14Hz{Assumeπ=3.14}

fm=2000Hz=2kHz

Hence, modulating frequency is 2kHz.


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