Question

A carrier wave of frequency 2 MHz, is amplitude modulated by a given message signal. The‘message signal’ contains a mix–up of audio signals of frequencies 750 Hz, 1200 Hz and 5000 Hz. 

The bandwidth of the resultant AM carrier wave can be

(1) 4.250 kHz 

(2) 10 kHz 

(3) 1995.750 kHz 

(4) 2004.250 kHz

Answer 1

Correct option: (2) 10 kHz

Explanation: 

The Am carrier wave has, in addition to its own carrier frequency, two side bands of frequencies (ω_c –ω_m) and (ω_c +ω_m). The ‘bandwidth’, of a signal, equals the difference between its highest frequency and its lowest frequency. Hence the bandwidth, of the AM carrier wave, is

Its bandwidth is, therefore, twice the frequency of the modulating (message) signal. In the given case, the message signal contains 5000 Hz as its highest frequency. Hence the bandwidth can be taken as 10 kHz.