Question

Problem 2 Consider the following two mechanical waves traveling in opposite directions in the same medium: yr(x, t) 10 cos(10t - 10x) cm y2(x, t) 10 sin(10t + 10x) cm where x is in centimeters. It can be said that the waves interfere with each other constructively where their superposition, [ysl = y, + y2l, is at a maximum and that the waves interfere with each other destructively where ly,l is at a minimum. Answer the following: a) For time t =, find the smallest positive value for a location x (meaning the location closest to the origin) where the waves interfere with each other constructively and note the corresponding value of lys at this location b) For time t =s, find the smallest positive value for a location x where the waves interfere with each other destructively and note the corresponding value of lys at this location 20 20

Answer 1

4,(a,t) 10 (ot -1o) Givern Sin 10 (1ot + 10) t Givern 20 y.(7,4) 1D Cos 20 10x) TT JD Sin 1Dsio (i0. 10a) (t-T) 20 10 No w + 0 Coslon 9 Xe Sin (0) 1Caslio

Sirloa) Cos 45 s02) Sin45 s 10 Sin(45+ 102) (4.5101)-1 ye marim um when Sin 45t 107 90 4 io raotans Given t T 40 S0 Shauld be n ndians then 10/2 sin 90 Ys 102 Sin 4.5t10)-0 minumum when 45101= Sin(o) Since Sin Co) 270 180 +10n =T 311 T = 40 1012 Sinle0 Nor %s
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