Question

MESSAGE MY INSTRUCTOR FULL SCREEN PRINTER VERSION BACK NEXT Chapter 17, Problem 05 Two waves are traveling in opposite directions on the same string. The displacements caused by the individiual waves are given by y1-(27.0 mm)sin(7.54nt 1.52nx) and y2-(33.0 mm)sin(2.94nt +0.404nx). Note that the phase angles (7.54nt 1.52nx) and (2.94nt+0.404nx) are in radians, t is in seconds, and x is in meters. At t-2.80 s, what is the net displacement (in mm) of the string at (a)x -2.27 m and (b) x 2.93 m? Be sure to include the algebraic sign (+ or-) with your answers Units (a) Number (b) Number Click if you would like to Show Work for this question: Units Open Show Work LINK TO TEXT LINK TO TEXT

Answer 1

Please let me know if there is any mistake

This is a simple plug in type question,

The resultant displacement is given as

y(x,t) = (27)sin(7.54$\pi$t - 1.52$\pi$x) + (33)sin(2.94$\pi$t + 0.404$\pi$x)

Now, just put given value of t and x for each case

for t = 2.80 and x = 2.27 ,

y(x,t) = (27)sin(7.54*3.14*2.80 - 1.52*3.14*2.27) + (33)sin(2.94*3.14*2.80 + 0.404*3.14*2.27)

y(x,t) = -23.9544 - 14.466

y(x,t) = - 38.42 m

-----------------------------------------------------------------------

now, for t = 2.80 and x = 2.93

y(x,t) = (27)sin(7.54*3.14*2.80 - 1.52*3.14*2.93) + (33)sin(2.94*3.14*2.80 + 0.404*3.14*2.93)

y(x,t) = 24.05 -31.71

y(x,t) = -7.666 m