Question

Two sinusoidal waves in a string are defined by the wave functions y1 = 1.60sin(16.0x − 30.0t) y2 = 1.60sin(26.0x − 41.0t) where x, y1, and y2 are in centimeters and t is in seconds. (a) What is the phase difference between these two waves at the point x = 5.00 cm at t = 2.00 s? 164 Correct: Your answer is correct. °

(b) What is the positive x value closest to the origin for which the two phases differ by ±π at t = 2.00 s? (At that location, the two waves add to zero.) 0.629 Incorrect: Your answer is incorrect. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. cm

Answer 1

Frad: 57.299 LLL a Wave Panchons Y,= 1.60 Sin [1686-304) Y2= 1.60 Sin [268-414) Phase difference : 18,-02) = 1862-30t)- (262-411)|| plugging a=5cm ; t=25 = |(1645 – 30x2)-(2645 - 41x2) = 1680-60)-(130-82)) = 120-48|| = 28 rad: = 28x57.240 - 1604.12° moy 1604 Since phase difference has to be < 360° .. 1604.2 - 4x360 = 1604.2-1440-164° (b) phase of the first wave after 2sec = M 16x-60 phase of the second wave after 2sec = 26x -82 Their prese difference - (262-82)-(16x-60) 102-22 = [2KET 10x = 22+(2k +1) a 1: 3.1416 = [7+26*Ja heast value of 100 is when K=-2 :) 100C = [7-5] D = 20 &= 215 = 2*3.1416 6.29 22 - 7.00 3:14 10