Final answer:
The FM waveform with a carrier frequency of 2 MHz, modulation sensitivity of k = 100 Hz/V, and modulating signal s(t)=100cos(300πt) volts will occupy a frequency band from 1.990 MHz to 2.010 MHz.
Step-by-step explanation:
The question involves calculating the approximate band of frequencies occupied by an FM waveform given a carrier frequency of 2 MHz, a modulation sensitivity of k = 100 Hz/V, and a modulation signal s(t)=100cos(300πt) volts. To solve this, we can use the modulation index, which is calculated as the maximum deviation of the frequency (Δf) divided by the maximum modulating frequency (fm).
Firstly, the maximum amplitude of the voltage signal s(t) is 100 volts, since the cosine function varies between -1 and 1. Given k = 100 Hz/V, the maximum deviation Δf will be k multiplied by the maximum amplitude of s(t), which equals 100 volts. Thus, Δf = 100 Hz/V * 100 V = 10,000 Hz or 10 kHz.
The maximum modulating frequency fm can be determined from the modulation signal s(t). It is given by the highest frequency component of the modulating signal, which in this case is 150 Hz. Hence, the signal will occupy a range from (2 MHz - 10 kHz) to (2 MHz + 10 kHz), giving us a band of frequencies from 1.990 MHz to 2.010 MHz.