Wave Interference and superposition

  • Thread starter Destrio
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Consider two point sources S1 and S2 which emit waves of the same frequency and amplitude A. The waves start in the same phase, and this phase relation at the sources is maintained throughout time. Consider point P at which r1 is nearly equal to r2.

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
 

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