What is the band width in amplitude modulation ?

Options

A. Equal to frequency of audio signal
B. Double the frequency of audio signal
C. Half the frequency of carrier wave
D. Double the frequency of carrier wave

Answer

To determine the bandwidth in amplitude modulation (AM), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Amplitude Modulation (AM)**:
- In AM, a carrier wave is modulated by an audio signal (the message signal). The carrier wave has a frequency \( f_c \) and the audio signal has a frequency \( f_m \).

2. **Identifying Side Frequencies**:
- The AM wave generates two sidebands: the Upper Sideband (USB) and the Lower Sideband (LSB).
- The frequencies of these sidebands are given by:
- Lower Side Frequency (LSF) = \( f_c - f_m \)
- Upper Side Frequency (USF) = \( f_c + f_m \)

3. **Calculating Bandwidth**:
- The bandwidth (BW) of the AM signal is defined as the difference between the upper and lower side frequencies:
\[ BW = USF - LSF \]
- Substituting the expressions for USB and LSB:
\[ BW = (f_c + f_m) - (f_c - f_m) \]
- Simplifying this expression:
\[ BW = f_c + f_m - f_c + f_m = 2f_m \]

4. **Conclusion**:
- Therefore, the bandwidth of an amplitude-modulated wave is twice the frequency of the audio signal.
- Hence, the correct answer is that the bandwidth in amplitude modulation is **double the frequency of the audio signal**.

### Final Answer:
The bandwidth in amplitude modulation is **double the frequency of the audio signal**.

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