An audio signal given by `e_(s)=15sin 2pi(2000t)` modulates a carrier wave given by `e_(s)=60sin 2pi (100,000t)`. If calculate (a) Percentage modulation (b) Frequency spectrum of the modulated wave.

Explanation

By comparing the given equations of signal and carrier with their standard form
`e_(s)= E_(s)sin Omega _(s)t= E_(s)sin2pif_(s)t`
`e_(c)= E_(c)sinomega_(c)t= E_(c) sin2pif_(c)t`
we have signal frequency `F_(s)= 2000Hz` and carrier frequency `f_(c)= 100, 000Hz`
The frequencies present in modulated wave
(i) `f_(c)= 100, 000Hz= 100kHz`
(ii) `f_(c)-f_(s)= 100,000-2000= 98kHz`
(iii) `f_(c)+ f_(s)= 100kHz+ 2kHz=102 kHz`
Therefore, frequency spectrum of modulated wave extends from 98kHz to 102 kHz is called band width.