Question

Without doing the calculation, say which are the only two non-zero spectral lines of X( m) if the main period of the corresponding temporal signal x[n], of period N = 16, is given by: x[n]=[10 5 10 5 10 5 10 5 10 5 10 5 10 5 10 5];

Answer 1

The question pertains to wave characteristics such as amplitude, wavelength, velocity, and period, which are fundamental concepts in Physics when describing waves and their interference patterns.

Step-by-step explanation:

The student is asking about the characteristics of waves and their spectral lines, which falls within the realm of Physics. Specifically, the question relates to wave functions and how they describe waves in terms of amplitude, wavelength, velocity, period, and phase shifts. These terms help to understand various properties of waves, which is fundamental in wave physics.

For sinusoidal waves, the amplitude is the maximum displacement from the equilibrium position, the period (T) is the time it takes for one complete cycle of the wave, the wavelength (λ) is the distance over which the wave's shape repeats, and the velocity (v) is the speed at which the wave travels through a medium. The wavelength and frequency (f) are inversely related through the formula v = fλ.

When dealing with wave superposition, such as when two waves interfere, the resultant wave properties depend on the individual waves' amplitudes, wavelengths, frequencies, and phase differences. The concept of nodes—points where the resultant wave always has zero amplitude—is significant in understanding standing waves and interference patterns.