Answer :

Let ω_{c} and ω_{s} be the respective frequencies of the carrier and signal waves.

Signal received at the receiving station, V = V_{1}cos(ω_{c} + ω_{s})t

Instantaneous Voltage of the carrier wave, V_{in} = V_{c} cos ω_{c}t

V.V_{in} = V_{1.}V_{c}{cos(ω_{c} + ω_{s})t. cos ω_{c}t}

= ( V_{1.}V_{c})/2 {2cos(ω_{c} + ω_{s})t. cosω_{c}t}

= ( V_{1.}V_{c})/2 [cos{(ω_{c} + ω_{s})t + ω_{c}t} + cos {{(ω_{c} + ω_{s})t - ω_{c}t }

= (V_{1.}V_{c})/2 [cos{(2ω_{c} + ω_{s})t} + cos ω_{s}t ]

As the receiving centre allows only high frequency signals to pass through it. Obstructs the low frequency signal ω_{s} Thus, at the receiving station, one can record the modulating signal **(V _{1}V_{c}/2).cosω_{s}t** , which is the signal frequency.

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