Final answer:
The resultant wave function from the interference of two waves is the algebraic sum of the individual waves, determined by their amplitude and phase difference, leading to a pattern of constructive and destructive interference.
Step-by-step explanation:
When considering the interference of two wave functions, such as y1 (x, t) = A sin (kx - wt) and y2 (x, t) = A sin (kx + wt + p), the resulting wave function is found by algebraically adding the two wave functions together. Employing the trigonometric identity sin(a ± β) = sin a cos β ± cos a sin β, the interference of these two waves can be described.
The superposition of these two waves will result in a wave function that represents the net displacement of the medium at each point along the x-axis, leading to a pattern of constructive and destructive interference. Points of constructive interference result in higher amplitude, whereas points of destructive interference can lead to cancellation of the waves.
Without providing the exact mathematical resultant wave function, as the question did not provide all necessary parameters, we understand that the principles governing this phenomenon are based on the superposition of waves and their phase differences. The resultant wave function would thus depend on both the amplitude (A) and the phase difference (p) represented in the original wave functions.