A carrier is simultaneously amplitude-modulated by two sinusoidal tones with modulation indices m1 = 0.4 and m2 = 0.3. What is the resultant (total) modulation index for the AM signal?

Introduction / Context:
In multi-tone amplitude modulation, each tone contributes its own sidebands. The overall modulation depth must consider the combined effect to assess power distribution, distortion risk (overmodulation), and detector linearity. Knowing how to compute the net modulation index avoids clipping and excessive envelope distortion.

Given Data / Assumptions:

• Two independent sinusoidal modulators with indices m1 = 0.4 and m2 = 0.3.
• Standard linear AM with independent tones.
• No phase correlation that would alter envelope peak beyond RMS combination.

Concept / Approach:

For independent sinusoidal modulations, the effective modulation index m_total is the root-sum-square of the individual indices: m_total = sqrt(m1^2 + m2^2). This reflects the combined RMS modulation depth. It is commonly used to ensure the total modulation does not exceed unity (to prevent envelope overmodulation and distortion in envelope detectors).

Step-by-Step Solution:

Verification / Alternative check:

Envelope simulation or phasor addition of sidebands yields identical conclusions for uncorrelated tones. Practical AM broadcast standards often keep combined indices below 1 to avoid audible distortion.

Why Other Options Are Wrong:

• 0.7: simple arithmetic sum; overestimates true combined index for independent tones.
• 0.35 or 0.1: incorrect combinations that do not follow RMS summing.
• 0.58: not the correct RMS for given values.

Common Pitfalls:

Summing indices linearly instead of by RMS; ignoring the overmodulation threshold when multiple program components are present.

Final Answer:

0.5