A carrier wave is modulated by a number of sine waves with modulation indices `0.1,0.2,0.3` The totaal modulation index (m) of the wave is

Options

A. `0.6`
B. `0.2`
C. `sqrt(0.14)`
D. `sqrt(0.07)`

Answer

To find the total modulation index \( m \) of a carrier wave modulated by multiple sine waves with given modulation indices, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Modulation Indices**:
The modulation indices given are:
- \( m_1 = 0.1 \)
- \( m_2 = 0.2 \)
- \( m_3 = 0.3 \)

2. **Use the Formula for Total Modulation Index**:
The total modulation index \( m \) can be calculated using the formula:
\[ m = \sqrt{m_1^2 + m_2^2 + m_3^2} \]

3. **Substitute the Values**:
Substitute the values of \( m_1, m_2, \) and \( m_3 \) into the formula:
\[ m = \sqrt{(0.1)^2 + (0.2)^2 + (0.3)^2} \]

4. **Calculate Each Square**:
Calculate the squares of each modulation index:
- \( (0.1)^2 = 0.01 \)
- \( (0.2)^2 = 0.04 \)
- \( (0.3)^2 = 0.09 \)

5. **Sum the Squares**:
Now, sum these squared values:
\[ 0.01 + 0.04 + 0.09 = 0.14 \]

6. **Take the Square Root**:
Finally, take the square root of the sum to find the total modulation index:
\[ m = \sqrt{0.14} \approx 0.374 \]

### Final Answer:
The total modulation index \( m \) of the wave is approximately \( 0.374 \).

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