The modulation index is m. The Instantaneous carrier voltage is represented by, vc = Vc sin 2π fct. The instantaneous modulating

Question

Suppose the carrier wave is modulated in accordance with the amplitude of a message signal. 

The modulation index is m. The Instantaneous carrier voltage is represented by, v_c = V_c sin 2π f_ct. The instantaneous modulating voltage is presented by, v_m = V_m sin 2π f_mt.

The bandwidth of the amplitude modulated wave is equal to,

Answer 1

Correct option: (1) 2f_m

Explanation: 

Instantaneous voltage of the amplitude modulated wave is represented by,

This implies that in addition to the original central frequency, there exist side bands in an amplitude modulated wave. The frequency of upper sideband is equal to, f_c + f_m. The frequency of lower sideband is equal to f_c – f_m. The bandwidth is the difference in frequency of the side bands, which is given by, 

Bandwidth = (f_c + f_m – f_c + f_m) = 2f_m