Mathematical treatment of the formation of a standing wave
Let the displacements of two travelling waves 1 and 2 at time t and position x be y1 and y2.
y1 = a sin (wt - kx) (say right-left)
y2 = a sin (wt + kx) (say left-right)
Therefore:
Note that this expression is composed of two terms:
(a) sin (wt) - this shows a varying amplitude with time at a particular place.
(b) cos (kx) - this shows a varying amplitude with position at a particular time.
