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) 500 Hz
(B) 2 Hz
(C) 250 Hz
(D) 498 Hz
(E) 502 Hz
Choose the correct answer from the options given below:
- A, D and E only
- A and B only
- A and C only
- A and D only
The Correct Option is A
Solution and Explanation
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.
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