Question

A carrier is simultaneously modulated by two sine waves with modulation indices of 0.3 and 0.4; then the total modulation index is:

• A. \( 1 \)
• B. \( 0.12 \)
• C. \( 0.5 \)
• D. \( 0.7 \)

Hint:

When multiple signals modulate a carrier wave, use the square root sum of squares formula: \[ m_t = \sqrt{m_1^2 + m_2^2} \] This accounts for the total impact of multiple modulation signals.

Answer 1

The Correct Option is C

Step 1: Understanding Modulation Index When a carrier wave is modulated by multiple signals, the total modulation index (\( m_t \)) is given by: \[ m_t = \sqrt{m_1^2 + m_2^2} \] where: - \( m_1 = 0.3 \) (first sine wave modulation index), - \( m_2 = 0.4 \) (second sine wave modulation index).
Step 2: Calculating the Total Modulation Index Substituting the given values: \[ m_t = \sqrt{(0.3)^2 + (0.4)^2} \] \[ m_t = \sqrt{0.09 + 0.16} \] \[ m_t = \sqrt{0.25} \] \[ m_t = 0.5 \]
Step 3: Evaluating the Options - \( 1 \) (Incorrect): This would be the case if additional modulation waves contributed more. - \( 0.12 \) (Incorrect): This is an incorrect calculation of modulation index. - \( 0.5 \) (Correct): This follows the standard formula for multiple modulation signals. - \( 0.7 \) (Incorrect): This would imply a different set of modulation indices.
Step 4: Conclusion Thus, the total modulation index is \( 0.5 \).