Discussion
What is the effect of doubling a PM signal's index at constant message frequency?
Answer: A
The bandwidth is \( 2f_m(1+\beta_p) \), so doubling the index from say 3 to 6 takes it from \( 8f_m \) to \( 14f_m \): a large increase but less than twofold, because of the unity term. Exact doubling would require the unity term to be negligible, which it is at very large index. No change would contradict the formula, and halving inverts it. Noticing that the unity term matters most at small index is the practical value of keeping the full expression.
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