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a) Show that the superposition of these two waves gives a wave whole amplitude Y varies with the position P approximately according to:

Y = (2A/r)cos(k/2)(r1-r2)

in which r = (r1+r2)/2.

b) Then show that total cancellation occurs when (r1-r2)=(n+.5)λ and total reinforcement occurs when r1-r2 = nλ

so initially we have

W1 = Asin(kx-wt-r1)

W2 = Asin(kx-wt-r2)

and we can use sinB + sinC = 2sin(.5)(B+C)cos(.5)(B-C)

to make them look like: [2Acos((r2-r1)/2)]sin(kx-wt-(r1+r2)/2)

but i believe that only works if they are always in phase

any help would but much appreciated, i've been stuck on this for a long time

thanks