Question

Chapter 16, Problem 037 GO These two waves travel along the same string: Y. - (3.82 mm) sin(1.960x - 430xt) Y2 - (5.64 mm) sin(1.9611X - 430t +0.780xrad). What are (a) the amplitude and (b) the phase angle (relative to wave 1) of the resultant wave? (c) If a third wave of amplitude 4.54 mm is also to be sent along the string in the same direction as the first two waves, what should be its phase angle in order to maximize the amplitude of the new resultant wave? (a) Number Units (b) Number Units (c) Number Units Click if you would like to Show Work for this question: Open Show Work

Answer 1

Given two waves equations: y = (3.82 mm )sin (1.967x - 430t) ya = (5.64 mm)sin (1.96TX - 430nt +0.780 grad) (a) The amplitude is, A = (3.82 mm +5.64 mm) =9.46mm (b) The phase of the angle is, @=0.780 1-0 =0.7807 c) Third wave of amplitude 4.54 mm is to be sent along the string in the same direction as the first two waves such that the net of the three waves has the greatest possible amplitude. Possible angle of the third wave is the resultant phase angle of first two waves. The phase angle is, Q = 0.7807 The amplitude is, A = 9.46 mm +4.54 mm =14 mm