A carrier wave of amplitude A is used to modulate (amplitude) the signal.Modulated signal amplitude swings from 0.1 A to 1.9A,calculate modulation index.`

Answer

To calculate the modulation index for the given modulated signal, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amplitudes**:
- The modulated signal amplitude swings from 0.1A to 1.9A.
- The maximum amplitude of the modulated signal (A_m) is 1.9A.
- The minimum amplitude of the modulated signal is 0.1A.

2. **Calculate the Amplitude of the Modulating Signal (A_m)**:
- The amplitude of the modulating signal (A_m) can be calculated as:
\[ A_m = \frac{(A_{max} - A_{min})}{2} \]
- Here, \( A_{max} = 1.9A \) and \( A_{min} = 0.1A \).
- Thus,
\[ A_m = \frac{(1.9A - 0.1A)}{2} = \frac{1.8A}{2} = 0.9A \]

3. **Calculate the Amplitude of the Carrier Wave (A_c)**:
- The amplitude of the carrier wave (A_c) is the average of the maximum and minimum amplitudes of the modulated signal:
\[ A_c = \frac{(A_{max} + A_{min})}{2} \]
- Therefore,
\[ A_c = \frac{(1.9A + 0.1A)}{2} = \frac{2.0A}{2} = 1.0A \]

4. **Calculate the Modulation Index (m)**:
- The modulation index (m) is given by the formula:
\[ m = \frac{A_m}{A_c} \]
- Substituting the values we found:
\[ m = \frac{0.9A}{1.0A} = 0.9 \]

### Final Answer:
The modulation index is **0.9**.