Question

Amplitude modulated wave is represented by V_AM = 10[1+0.4cos(2π×10⁴t] cos(2π×10⁷t). The total bandwidth of the amplitude modulated wave is:

• A. 10 kHz
• B. 20 MHz
• C. 20 kHz
• D. 10 MHz

Answer 1

The Correct Option is C

To determine the total bandwidth of the amplitude modulated (AM) wave given by the equation \( V_{\text{AM}} = 10[1 + 0.4\cos(2\pi \times 10^4 t)] \cos(2\pi \times 10^7 t) \), we need to examine the components of the signal.

The general form of an amplitude-modulated signal is \( V_{\text{AM}} = A_c[1 + m \cos(2\pi f_m t)]\cos(2\pi f_c t) \), where:

• \( A_c \) is the carrier amplitude.
• \( f_c \) is the carrier frequency.
• \( m \) is the modulation index.
• \( f_m \) is the modulating frequency.

From the given equation, we identify:

• Modulating frequency \( f_m = 10^4 \, \text{Hz} = 10 \, \text{kHz} \)
• Carrier frequency \( f_c = 10^7 \, \text{Hz} = 10 \, \text{MHz} \)

The total bandwidth of an amplitude modulated signal is calculated as:

B = 2f_m

Substituting the given value:

B = 2 \times 10 \, \text{kHz} = 20 \, \text{kHz}

Thus, the total bandwidth of the amplitude modulated wave is 20 kHz.