Question

Two waves are traveling in opposite directions on the same string. The displacements caused by the individiual waves are given by y1=(22.0 mm)sin(9.86πt - 1.52πx) and y2=(36.0 mm)sin(2.53πt + 0.330πx). Note that the phase angles (9.86πt - 1.52πx) and (2.53πt + 0.330πx) are in radians, t is in seconds, and x is in meters. At t = 3.20 s, what is the net displacement (in mm) of the string at (a) x = 2.31 m and (b) x = 2.93 m? Be sure to include the algebraic sign (+ or -) with your answers.

Answer 1

Approach used:- Here we use the superposition principle for addition of waves to find the net displacement of resultant wave at a given time and position,

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Put t 3.2s ao x2.31 m in Put t3.2s ano x- 2-31 m hn and we 2- So net displacement is, Put t - 3.2s ano x 2.43 m ln and we 2-.93 m n and we get 2 13.76 mn