Question

If the ratio of the maximum and minimum amplitudes of an amplitude modulated wave is 7:3, then the modulation index is

• A. 0.6
• B. 0.7
• C. 0.4
• D. 0.3

Hint:

Modulation Index = $\frac{A_{\text{max}} - A_{\text{min}}}{A_{\text{max}} + A_{\text{min}}}$.

Answer 1

The Correct Option is C

The modulation index ($\mu$) is given by: $$ \mu = \frac{A_{\text{max}} - A_{\text{min}}}{A_{\text{max}} + A_{\text{min}}} $$ Given $A_{\text{max}} : A_{\text{min}} = 7:3$, we can write $A_{\text{max}} = 7k$ and $A_{\text{min}} = 3k$ for some constant $k$. Then, $$ \mu = \frac{7k - 3k}{7k + 3k} = \frac{4k}{10k} = 0.4 $$