Question

Find the modulation index in the signal s(t) = 2 cos(2\π+ 200 t + k_a m(t)), where |m(t)| has a maximum of .1.

Answer 1

The modulation index for the signal s(t) is calculated by multiplying the constant k_a by the peak value of the modulating signal m(t), which is given as 0.1. Without the specific value of k_a, we cannot provide a numeric value for the modulation index.

Step-by-step explanation:

The modulation index is a parameter that represents the level of modulation applied to a carrier waveform in relation to the maximum value of the modulating signal. In the signal s(t) = 2 cos(2\pi + 200t + k_a m(t)), the modulation index is represented by the constant k_a multiplied by the peak value of the modulating signal m(t).

Since the maximum value of |m(t)| is given as 0.1, the modulation index \mu will be k_a times this maximum value. Thus, \mu = k_a \times 0.1. The exact value of k_a is not specified in the question, so we cannot provide a numeric value for the modulation index without further information.

Understanding modulation index is important as it affects the amplitude of the carrier signal and can influence the bandwidth and power requirements of the communication system.

Answer 2

The modulation index in the given signal is 0.05, or 5%.

Step-by-step explanation:

The modulation index of an amplitude modulated signal is given by the ratio of the maximum amplitude of the modulating signal to the amplitude of the carrier wave.

In the given signal s(t) = 2 cos(2π+ 200t + kₐₘ(t)), the maximum amplitude of the modulating signal |m(t)| is 0.1, and the amplitude of the carrier wave is 2. Therefore, the modulation index (β) can be calculated as β = |m(t)|/2.

Since we know that the maximum of |m(t)| is 0.1, we can directly find the modulation index:

β = 0.1 / 2 = 0.05, or 5%.

Your question is incomplete, but most probably the full question was:

Find the modulation index in the signal s(t) = 2 cos(2\π+ 200 t + kₐₘ(t)), where |m(t)| has a maximum of the carrier wave.