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Question

an audio signal of amplitude one fourth the ampltude of carrier wave is used in amplitude modulation what is modulation index

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Solution

Modulation index m can be given as the ratio of amplitude of the modulating wave A_M to amplitude of the carrier wave A_C.
$m = \frac{A_{M}}{A_{C}}$
As given A_M is one fourth of A_C,

A_M = 1/4 A_C
Therefore
$m = \frac{A_{M}}{4 A_{M}} m = \frac{1}{4} m = 0.25$

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