Two waves are traveling in opposite directions on the same string. The displacem

Question

Two waves are traveling in opposite directions on the same string. The displacements caused by the individual waves are given by y1 = (22.2 mm)sin(9.00t 1.25x) and y2 = (31.5 mm)sin(2.88t + 0.400x). Note that the phase angles (9.00t 1.25x) and (2.88t + 0.400x) are in radians, t is in seconds, and x is in meters. At t = 4.36 s, determine the net displacement (in mm) of the string for the following values of x. Be sure to include the algebraic sign (+ or ) with your answers.

(a) x = 2.28 m ANSWER

(b) x = 2.80 m ANSWER

Explanation / Answer

part a:

at x=2.28 m and t=4.36 seconds,

y1=22.2*sin(9*pi*4.36-1.25*pi*2.28) mm=20.888 mm

y2=31.5*sin(2.88*pi*4.36+0.4*pi*2.28) mm=-31.349 mm

total displacement=y1+y2=-10.461 mm

part b:

at x=2.8 m, t=4.36 seconds

y1=22.2*sin(9*pi*4.36-1.25*pi*2.8) mm=-16.183 mm

y2=31.5*sin(2.88*pi*4.36+0.4*pi*2.8) mm=-26.765 mm

total displacement=y1+y2=-42.948 mm

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