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 = (25.4 mm)sin(9.00?t ? 1.25?x) and y2 = (34.5 mm)sin(2.88?t + 0.400?x). Note that the phase angles (9.00?t ? 1.25?x) and (2.88?t + 0.400?x) are in radians, t is in seconds, and x is in meters. At t = 3.72 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 = 2.18 m
(b) x = 2.54 m

Explanation / Answer

a.)
y1=25.4 sin(9.00*pi*3.72-1.25*pi*2.18)=+25.23315 mm
y2=34.5 sin(2.88*pi*3.72+0.40*pi*2.18)=+17.71 mm

b). y1=25.4 sin(9.00*pi*3.72-1.25*pi*2.54)=+25.297 mm
y2=34.5 sin(2.88*pi*3.72+0.40*pi*2.54)=+20.68 mm

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