# Answer the Following Question. If a and B Represent the Maximum and Minimum Amplitudes of an Amplitude-modulated Wave, Write the Expression for the Modulation Index in Terms of a and B. - Physics

#### Question

Short Note

If A and B represent the maximum and minimum amplitudes of an amplitude-modulated wave, write the expression for the modulation index in terms of A and B.

#### Solution

Modulation index for an AM wave for which the maximum amplitude is 'a' while the minimum amplitude id 'b'.

Modulation index,

a_m = (E_m)/(E_c)  ...(1)

The maximum amplitude of the modulated wave, a = Ec + Em  ...(2)

The minimum amplitude of the modulated wave, b = Ec - Em ....(3)

From the above equations,

E_c = (a + b)/2 , E_m = (a - b)/2

From Equation 1 we get,

Thus, the modulation index is a_m = E_m/E_c = (((a - b))/2)/(((a + b))/2) = ((a - b))/((a + b)).

Concept: Amplitude Modulation
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