Question

An amplitude modulated wave is represented by,

v_AM = 4 (1 + 0.2 sin 314 t) sin (314 x 10² t)

For this wave, one can say that

(1) Frequency of the upper sideband is 5000 Hz; and frequency of the lower sideband is 50 Hz

(2) Frequency of the upper sideband is 100 Hz; and frequency of the lower sideband is 50 Hz

(3) Frequency of the upper sideband is 5050 Hz; and frequency of the lower sideband is 4950 Hz

(4) Frequency of the upper sideband is 314 x 10² Hz; and frequency of the lower sideband is 314 Hz

Answer 1

(3) Frequency of the upper sideband is 5050 Hz; and frequency of the lower sideband is 4950 Hz

According to the expression, 

Frequency of the modulating wave = f_m = 1/2π 314 = 50Hz

Frequency of the carrier wave = f_m = 1/2π (314 = 10²) = 5000 Hz

Therefore, 

Frequency of the upper sideband = f_c - f_m = 5050 Hz 

Frequency of the lower sideband = f_c - f_m = 4950 Hz