Amplitude of carrier wave and message wave are 5 unit and 3 unit resp. then ratio of maximum and minimum amplitude of modulated wave

Options

A. 2
B. 4
C. 6
D. 8

Answer

To solve the problem, we need to find the ratio of the maximum and minimum amplitudes of a modulated wave given the amplitudes of the carrier wave and the message wave.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Amplitude of the carrier wave (A_c) = 5 units
- Amplitude of the message wave (A_m) = 3 units

2. **Determine the Maximum Amplitude:**
- The maximum amplitude (A_max) of the modulated wave occurs during constructive interference, which is the sum of the amplitudes of the carrier and message waves.
- Formula:
\[ A_{max} = A_c + A_m \]
- Calculation:
\[ A_{max} = 5 + 3 = 8 \text{ units} \]

3. **Determine the Minimum Amplitude:**
- The minimum amplitude (A_min) of the modulated wave occurs during destructive interference, which is the difference between the amplitudes of the carrier and message waves.
- Formula:
\[ A_{min} = A_c - A_m \]
- Calculation:
\[ A_{min} = 5 - 3 = 2 \text{ units} \]

4. **Calculate the Ratio of Maximum to Minimum Amplitude:**
- The ratio of maximum amplitude to minimum amplitude is given by:
\[ \text{Ratio} = \frac{A_{max}}{A_{min}} \]
- Calculation:
\[ \text{Ratio} = \frac{8}{2} = 4 \]

5. **Conclusion:**
- The ratio of the maximum and minimum amplitude of the modulated wave is 4.

### Final Answer:
The ratio of maximum and minimum amplitude of the modulated wave is **4**.

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