The amplitude of $15 \sin (1000 \pi t )$ is modulated by $10 \sin (4 \pi t )$ 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:
The amplitude of $15 \sin (1000 \pi t )$ is modulated by $10 \sin (4 \pi t )$ 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:
Show Hint
- B Only
- A and B Only
- A, D and E Only
- A Only
The Correct Option is C
Approach Solution - 1
Modulating wave frequency
Approach Solution -2
The modulated signal consists of a carrier frequency and sideband frequencies.
The carrier wave frequency is given by:
\[ V_c = \frac{100\pi}{2\pi} = 500 \, \text{Hz} \]
The modulating wave frequency is:
\[ V_m = \frac{4\pi}{2\pi} = 2 \, \text{Hz} \]
The modulated signal contains the frequencies:
\[ V_c - V_m = 500 - 2 = 498 \, \text{Hz}, \quad V_c + V_m = 500 + 2 = 502 \, \text{Hz} \]
Thus, the frequencies are 498 Hz and 502 Hz.
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Concepts Used:
Waves
Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.
Types of Waves:
Transverse Waves -
Waves in which the medium moves at right angles to the direction of the wave.
Examples of transverse waves:
- Water waves (ripples of gravity waves, not sound through water)
- Light waves
- S-wave earthquake waves
- Stringed instruments
- Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.
Longitudinal Wave -
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.
Examples of longitudinal waves:
- Sound waves
- P-type earthquake waves
- Compression wave