Answer:
Modulating index for an AM wave is defined as the ratio of change in the amplitude of the carrier wave to the amplitude of the original carrier wave. \[\text{ }\!\!\mu\!\!\text{ =}\frac{\text{Change in the amplitde of carrier wave}}{\text{Amplitude of the original carrier wave}}\] \[=\frac{{{A}_{m}}}{{{A}_{c}}}\] When a and b are the maximum and minimum amplitudes of the AM wave, then \[{{A}_{m}}=\frac{a-b}{2}\] and \[{{A}_{c}}=a-{{A}_{m}}=a-\frac{a-b}{2}=\frac{a+b}{2}\] \[\therefore \] \[\mu =\frac{{{A}_{m}}}{{{A}_{c}}}=\frac{(a-b)/2}{(a+b)/2}=\frac{a-b}{a+b}\]
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