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Amplitude of a Wave

A 10 MHz si...

Question

A $10$ MHz sinusoidal carrier wave of amplitude $10$ mV is modulated by a $5$ kHz sinusoidal audio signal wave of amplitude $6$ mV. Find the frequency components of the resultant modulated wave and their amplitudes.

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Solution

Data given:
Frequency of carrier= $f_{c} = 10 M H z$
frequency of the signal $= f_{s} = 5 K H z = 0.005 M H z$
Amplitude of carrier signal $= E_{c} = 10 m V$
Amplitude of audio signal $= E_{s} = 6 m V$
$s o l u t i o n$
The modulated carrier wave contains the folloeing frequencies:
Original carrier wave of frequency $= f_{c} = 10 M H z$
upper side band, $f_{c} + f_{s} = 10 + 0.005 = 10.005 M H z$
Lower side band frequency $f_{c} - f_{s} = 10 - 0.005 = 9.995 M H z$
The modulation factor $μ = \frac{A_{m}}{A_{c}} = \frac{6}{10} = 0.6$
Amplitude = $\frac{μ A_{c}}{2} = 3 m V$

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