Answer :

Let ωc and ωs be the respective frequencies of the carrier and signal waves.

Signal received at the receiving station, V = V1cos(ωc + ωs)t

Instantaneous Voltage of the carrier wave, Vin = Vc cos ωct

V.Vin = V1.Vc{cos(ωc + ωs)t. cos ωct}

= ( V1.Vc)/2 {2cos(ωc + ωs)t. cosωct}

= ( V1.Vc)/2 [cos{(ωc + ωs)t + ωct} + cos {{(ωc + ωs)t - ωct }

= (V1.Vc)/2 [cos{(2ωc + ωs)t} + cos ωst ]

As the receiving centre allows only high frequency signals to pass through it. Obstructs the low frequency signal ωs Thus, at the receiving station, one can record the modulating signal (V1Vc/2).cosωst , which is the signal frequency.

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