Amplitude modulated wave is represented by VAM = 10[1 + 0.4 cos(2π × 104t] cos(2π × 107t). The total bandwidth of the amplitude modulated wave is :
Amplitude modulated wave is represented by VAM = 10[1 + 0.4 cos(2π × 104t] cos(2π × 107t). The total bandwidth of the amplitude modulated wave is :
- 10 kHz
- 20 MHz
- 20 kHz
- 10 MHz
The Correct Option is C
Approach Solution - 1
To determine the total bandwidth of the given amplitude modulated wave, we begin by understanding the formula for an amplitude modulated (AM) signal. The given equation is:
\(V_{AM} = 10 \left[ 1 + 0.4 \cos(2\pi \times 10^4 t) \right] \cos(2\pi \times 10^7 t)\)
where:
- The carrier frequency, \(f_c\), is \(10^7\) Hz or 10 MHz.
- The modulating frequency, \(f_m\), is \(10^4\) Hz or 10 kHz.
The general formula for an AM wave is:
\(V_{AM} = [A + A_m \cos(2\pi f_m t)] \cos(2\pi f_c t)\)
where \(A_m\) is the modulation index.
The total bandwidth of an AM signal is given by:
\(BW = 2f_m\)
Given that the modulating frequency \(f_m = 10\text{ kHz}\), the total bandwidth \(BW\) is calculated as:
\(BW = 2 \times 10\text{ kHz} = 20\text{ kHz}\)
Thus, the total bandwidth of the amplitude modulated wave is 20 kHz, which matches the given correct answer.
Approach Solution -2
The correct answer is (C) : 20 kHz
Bandwidth = 2 × fm
= 2 × 104 Hz
= 20 kHz
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Concepts Used:
Electromagnetic waves
The waves that are produced when an electric field comes into contact with a magnetic field are known as Electromagnetic Waves or EM waves. The constitution of an oscillating magnetic field and electric fields gives rise to electromagnetic waves.
Types of Electromagnetic Waves:
Electromagnetic waves can be grouped according to the direction of disturbance in them and according to the range of their frequency. Recall that a wave transfers energy from one point to another point in space. That means there are two things going on: the disturbance that defines a wave, and the propagation of wave. In this context the waves are grouped into the following two categories:
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- Transverse waves: A wave is called a transverse wave when the disturbances in the wave are perpendicular (at right angles) to the direction of propagation of the wave.