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 of finding the ratio of the maximum and minimum amplitude of a modulated wave formed by a carrier wave and a message wave, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amplitudes**:
- The amplitude of the carrier wave (A1) is given as 5 units.
- The amplitude of the message wave (A2) is given as 3 units.

2. **Determine Maximum Amplitude**:
- The maximum amplitude of the modulated wave occurs during constructive interference, where the two waves are in phase.
- The formula for maximum amplitude (A_max) is:
\[ A_{max} = A1 + A2 \]
- Substituting the values:
\[ A_{max} = 5 + 3 = 8 \text{ units} \]

3. **Determine Minimum Amplitude**:
- The minimum amplitude of the modulated wave occurs during destructive interference, where the two waves are out of phase.
- The formula for minimum amplitude (A_min) is:
\[ A_{min} = A1 - A2 \]
- Substituting the values:
\[ A_{min} = 5 - 3 = 2 \text{ units} \]

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

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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