Question

The maximum amplitude for an amplitude modulated wave is found to be 12 V while the minimum amplitude is found to be 3 V. The modulation index is 0.6x where x is ________ .

Hint:

The modulation index, also known as modulation depth, is a measure of how much the carrier wave's amplitude is varied by the message signal. It's a dimensionless quantity that typically ranges from 0 to 1 for standard AM.

Answer 1

Correct Answer: 1

The formula for the modulation index ($\mu$) in amplitude modulation is given by the maximum ($A_{max}$) and minimum ($A_{min}$) amplitudes of the modulated wave.
$\mu = \frac{A_{max} - A_{min}}{A_{max} + A_{min}}$.
We are given the values:
$A_{max} = 12$ V.
$A_{min} = 3$ V.
Substitute these values into the formula:
$\mu = \frac{12 - 3}{12 + 3} = \frac{9}{15}$.
Simplifying the fraction gives:
$\mu = \frac{3}{5} = 0.6$.
The problem states that the modulation index is $0.6x$.
So, we have the equation $0.6x = 0.6$.
Solving for x, we get:
$x = \frac{0.6}{0.6} = 1$.