10 10) let the phase
difference between the two displacements be f Thus, if the displacement
produced by S1 is given by
y1 = a cos wt
then, the displacement produced by S2 would be
y2 = a cos (wt + f)
and the resultant displacement will be given by
y = y1 + y2
   = a [cos wt + cos (wt +f)]
   = 2 a cos (f/2) cos (wt + f/2)
The amplitude of the resultant displacement is 2a cos (f/2) and
therefore the intensity at that point will be
I = 4 I0 cos2 (f/2)
(10 11)
If f = 0, ± 2 p, ± 4 p,… which corresponds to the condition given by
Eq