If` omega_c` and `omega_m` are angular frequencies of carrier wave and modulating signal respectively, then Band width of amplitude modulated waves is equal to

Options

A. `(omega_c+omega_m)/2`
B. `2omega_m`
C. `2omega_c`
D. `(omega_c-omega_m)/2`

Answer

To find the bandwidth of amplitude modulated (AM) waves, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Frequencies**:
- Let `ω_c` be the angular frequency of the carrier wave.
- Let `ω_m` be the angular frequency of the modulating signal.

2. **Identifying the Frequency Components**:
- In amplitude modulation, the modulated signal contains frequency components at:
- Upper side frequency: `ω_c + ω_m`
- Lower side frequency: `ω_c - ω_m`

3. **Calculating the Bandwidth**:
- The bandwidth of the AM wave can be calculated by finding the difference between the upper and lower side frequencies:
\[ \text{Bandwidth} = (\omega_c + \omega_m) - (\omega_c - \omega_m) \]

4. **Simplifying the Expression**:
- Simplifying the above expression gives:
\[ \text{Bandwidth} = \omega_c + \omega_m - \omega_c + \omega_m = 2\omega_m \]

5. **Conclusion**:
- Therefore, the bandwidth of the amplitude modulated wave is equal to \( 2\omega_m \).

### Final Answer:
The bandwidth of amplitude modulated waves is \( 2\omega_m \).

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