Question

An AM wave is given by \(C(t)=10[1+0.4\cos(10^4 t)+0.3\cos(10^5 t)]\cos(10^6 t)\). The modulation index of the envelope is

• A. \(0.4\)
• B. \(0.5\)
• C. \(0.3\)
• D. \(0.9\)

Hint:

For multiple tones, modulation index is RMS sum.

Answer 1

The Correct Option is B

Concept: Total modulation index for multiple signals: \[ m = \sqrt{m_1^2 + m_2^2} \]

Step 1: Identify indices \[ m_1 = 0.4,\quad m_2 = 0.3 \]

Step 2: Apply formula \[ m = \sqrt{(0.4)^2 + (0.3)^2} \]

Step 3: Calculate squares \[ m = \sqrt{0.16 + 0.09} \]

Step 4: Simplify \[ m = \sqrt{0.25} = 0.5 \]

Step 5: Conclusion \[ \boxed{0.5} \]

Final Answer: \[ \boxed{(B)} \]