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 waves given the angular frequencies of the carrier wave (ω_c) and the modulating signal (ω_m), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components**:
- The carrier wave has an angular frequency denoted by ω_c.
- The modulating signal has an angular frequency denoted by ω_m.

2. **Identify the Sidebands**:
- In amplitude modulation, the modulated signal creates two sidebands:
- The Upper Sideband (USB) frequency is given by:
\[ \text{USB} = \omega_c + \omega_m \]
- The Lower Sideband (LSB) frequency is given by:
\[ \text{LSB} = \omega_c - \omega_m \]

3. **Calculate the Bandwidth**:
- The bandwidth (BW) of the amplitude modulated signal is defined as the difference between the maximum frequency (USB) and the minimum frequency (LSB):
\[ \text{Bandwidth} = \text{USB} - \text{LSB} \]
- Substituting the expressions for USB and LSB:
\[ \text{Bandwidth} = (\omega_c + \omega_m) - (\omega_c - \omega_m) \]

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

5. **Final Result**:
- Therefore, the bandwidth of amplitude modulated waves is:
\[ \text{Bandwidth} = 2\omega_m \]

### Conclusion:
The bandwidth of amplitude modulated waves is equal to \( 2\omega_m \).