Which of the following pairs of wave equations represents a pair of waves that can produce a stable,

Question

Which of the following pairs of wave equations represents a pair of waves that can produce a stable, sustained interference pattern when superposed?

Professor PC Thomas Classes · Answer

(b) : For obtaining a stable and sustained interference pattern, the two superimposing waves must be highly coherent. This fundamental condition strictly dictates that they must have the exact same frequency (and wavelength) and maintain a completely constant phase difference over time. The waves $y_1 = A \sin(\omega t - kx)$ and $y_2 = A \cos(\omega t - kx) = A \sin(\omega t - kx + \pi/2)$ share the same angular frequency $\omega$ and have a constant time-independent phase difference of $\pi/2$.