Final answer:
To calculate the percentage modulation of an amplitude-modulated signal, use the modulation index formula: (Amplitude of modulating signal / Amplitude of carrier wave) × 100. For the given example with a modulating signal of 2cos(π103t) and a carrier wave of 10cos(2π104t), the percentage modulation is 20%.
Step-by-step explanation:
To determine the percentage modulation of an amplitude-modulated signal, we need to understand the terms modulating signal and carrier wave. In this example, the unsuppressed carrier AMA message signal is 2cos(π103t) Volts, which acts as the modulating signal, and the carrier wave is 10cos(2π104t) Volts. The percentage modulation, also known as the modulation index, is the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave, multiplied by 100 to get a percentage.
To calculate the modulation index (m), use the formula m = (Amplitude of modulating signal / Amplitude of carrier wave) × 100. In this case, it is (2 / 10) × 100 = 20%. This shows that the percentage modulation of the given signal is indeed 20%.