Final answer:
The fundamental frequency of x(t) is 50 Hz and the corresponding period is 0.02 s. The electromagnetic wave E has an amplitude of 30, a frequency of 6.37×105 Hz, and a period of approximately 1.57×10-6 seconds.
Step-by-step explanation:
The periodic signal, x(t), is composed of three signals with different frequencies. To find the fundamental frequency of x(t), we look for the greatest common divisor of the signal frequencies. Frequencies present in the signal are 150 Hz, 400 Hz, and 100 Hz. The greatest common divisor of these frequencies is 50 Hz, which is the fundamental frequency. The fundamental frequency corresponds to the lowest frequency and hence, the longest period of the signal. The period of a signal is the inverse of the frequency, so the period T of the fundamental frequency is T = 1/f. For a fundamental frequency of 50 Hz, the period is T = 1/50 s, or 0.02 s.
In the case of the electromagnetic wave E = (30) sin (4.0×106t), the amplitude is the coefficient in front of the sine function, which is 30. The angular frequency ω is 4.0×106 rad/s. To find the frequency, we use the formula ω = 2πf. Therefore, the frequency f is ω/(2π), which gives us a frequency of 6.37×105 Hz. The period T is the inverse of the frequency, hence T = 1/f, which is approximately 1.57×10-6 seconds or 1.57 microseconds.