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

(a) Signal Amplitude, `B=15`
Carrier amplitude, `A=60" "m=B/A=(15)/(60)=0.25`
`:.` Percentage modulation `=0.25xx100=25%`
(b) By comparing the given equations of signal and carrier with their standard form `e_(s)=E_(s)sin omega_(s)t=E_(s)sin 2pif_(s)t` and `e_(c)=E_(c)sin omega_(c)t=E_(c)sin2pi f_(c)t`
we have signal frequency `f_(s)=2000Hz` and carrier frequency `f_(c)=100,000` Hz
The frequencies present in modulated wave
(i) `f_(c)=100,000` Hz = 100 kHz
(ii) `f_(c)-f_(s)=100,000-2000=98` kHz
(iii)`f_(c)+f_(s)=100` kHz + 2kHz = 102 kHz
Therefore, frequency spectrum of modulated wave extends from 98kHz to 102 kHz is called band width.