Question

A message signal of frequency $5 \,kHz$ is used to modulate a carrier signal of frequency $2\, MHz$ The bandwidth for amplitude modulation is:

• A. $10 \,kHz$
• B. $2.5 \,kHz$
• C. $20\, kHz$
• D. $5\, kHz$

Answer 1

The Correct Option is A

To determine the bandwidth required for amplitude modulation, we need to use the concept of sidebands produced during modulation. In amplitude modulation (AM), the bandwidth \(B\) is determined by the frequency of the message signal.

The formula for bandwidth in amplitude modulation is:

\(B = 2 \times f_{m}\)

where \(f_{m}\) is the frequency of the message signal.

Given:

• Frequency of the message signal, \(f_{m} = 5 \, \text{kHz}\)

Let's substitute the given value into the formula:

\(B = 2 \times 5 \, \text{kHz} = 10 \, \text{kHz}\)

Thus, the bandwidth required for amplitude modulation is \(10 \, \text{kHz}\).

This corresponds to the correct answer: $10 \,kHz$.

By understanding these calculations, we can determine that the chosen answer is correct. Other options are incorrect because they do not satisfy the condition of doubling the message signal frequency to find bandwidth in amplitude modulation.