Question

The amplitude of 15sin(1000πt) is modulated by 10sin(4πt) signal. The amplitude modulated signal contains frequency(ies) of
(A) 500 Hz 
(B) 2 Hz  
(C) 250 Hz  
(D) 498 Hz  
(E) 502 Hz 
Choose the correct answer from the options given below: 

• A. A, D and E only
• B. A and B only
• C. A and C only
• D. A and D only

Answer 1

The Correct Option is A

Solution:
Carrier signal: $15 \sin(1000 \pi t)$
Modulating signal: $10 \sin(4 \pi t)$

The general form of a sinusoidal wave is $A \sin(2 \pi f t)$, where $A$ is the amplitude, $f$ is the frequency, and $t$ is time.

1. Carrier signal frequency $(f_c)$:
$$ 2 \pi f_c = 1000 \pi $$ $$ f_c = \frac{1000 \pi}{2 \pi} = 500 \text{ Hz} $$

2. Modulating signal frequency $(f_m)$:
$$ 2 \pi f_m = 4 \pi $$ $$ f_m = \frac{4 \pi}{2 \pi} = 2 \text{ Hz} $$

In amplitude modulation, the modulated signal contains the carrier frequency and two sideband frequencies:
 

Carrier frequency $(f_c) = 500 \text{ Hz}$

Lower sideband frequency $(f_c - f_m) = 500 \text{ Hz} - 2 \text{ Hz} = 498 \text{ Hz}$

Upper sideband frequency $(f_c + f_m) = 500 \text{ Hz} + 2 \text{ Hz} = 502 \text{ Hz}$

The frequencies present in the amplitude modulated signal are:
 

500 Hz (1)

498 Hz (4)

502 Hz (5)

Therefore, the correct answer is (4) (1), (4) and (5) only.