An audio signal given by `e_(s)=15 sin2pi(200t)` modulates a carrier wave given by `e_(s)=60 sin 2pi(100,000t)`. If calculate
(`a`) Percent 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)sinomega_(s)t=E_(s)sin2pif_(s)t` and `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=102kHz`
Therefore, frequency spectrum of modulated wave extends from `98kHz` to `102kHz` is called bandwidth.