Answer Happy

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Problem 3 [20 points) This problem is composed into two independent parts. Part 1 (10 points) For parts a), b) and c) of the below question, fill in the empty boxes with your answer (YOUR ANSWER MUST BE ONLY A NUMBER; DO NOT WRITE UNITS; DO NOT WRITE LETTERS). Two parallel waves travelling together are represented by the following functions: E1 E, sin(wt+al) and E2 = Eo2sin(wt + a2), with: E01 = 24 V/m, E02 = 88 V/m, w=161 rad/s, • Q1 = 0.2977 rad, Q2 =1.08 rad. a) [5 points) Find the resultant amplitude E, for the superposition of the two waves. V/m Eo = b) [4 points] The expression of the resultant wave for the superposition of E1 and E2 is of the form E= Eosin(wt + a). Find tan(a). tan(a) c) (1 point] Consider tan(a)=1.912. Deduce a. rad
Part 2 (10 points) Figures a and b below show the superposition of : • the waves E, and Ey, both propagating along the x-direction. the waves Ez and E4, both propagating along the x-direction. . 20 -AAA AN 10 Figure a Ez x(m) -10 -20+ 1 1 1 0 2 4 6 10 12 14 20 E3 10 Figure b 0 x(m) -10 E4 -20 0 2 8 10 12 14 For each part of the below question, choose one correct answer from the multiple choices. a) (5 points) E, and E, are: Oin phase Oout of phase Osuperposing destructively None of the above b) [5 points] Ez and E4 are: Oout of phase Oin phase Osuperposing constructively ONone of the above
= Chapter 7 c = 3 x 108 m/s H. = 12.56 x 10-7 T.m/A Eo = 8.85 x 10-12 C2/N. m2 = m € h = 6.626 x 10-34 J:s = 29 = 1f f= w = 2nf = 27 n 등지 21 20 k V= = = II 2= λ n = Optical Path Length (OPL): OPL = { nixi Addition of waves of the same frequency: E = {1+1 Eoisin(ai – wt) Ez = 27=1 Eði + 2]>iX?=1 Eoi Eojcos(ai – a;) 21=1 Eoi sin aſ tan a 21-1 Eoi cosa = Σ=1 in di Standing Waves: E(x, t) = 2E, sin(kx) cos(wt) 211 8 = (az - Q1) = -1 λο Distance between successive nodes (antinodes and nodes): d = Position of nodes: x = n; where n = 0,1, 2, ... Position of antinodes: x = (n + 1) where n = 0,1,2,... fbeat = \f1-f21 1,λ -