(a) Use the graphs to determine the displacement equation, that is, for the wave

Question

(a) Use the graphs to determine the displacement equation, that is, for the wave. (Use the following as necessary: x and t. Assume SI units. Do not enter units in your expression.)

D(x, t) = ??

(b) What is the speed of the wave, and in which direction is the wave travelling?

magnitude = ?? m/s direction = ?? Jennifer Aniston Destrc +xVw Assignment 12-Chapter xYeChegg Study; Guided Solx -> C D www.webassign.net/web/Student/Assignment-Responses/last?dep= 13202815 4. +-/3 points HawkPSE1 14.P.052. My Notes Ask Your Teacher A one-dimensional wave is traveling along the x-axis in the positive direction. The graph in the figure below shows the displacement versus position for the wave at t = 3.0 s D (x) (m) 0.15 0.10 0.05 x (m) 10 6 8 -0.05 -0.10 -0.15 The graph in the figure below shows the displacement versus time graph of the wave at x = 1.5 m D (x) (m) 0.15 0.10 0.05 t (s) 10 6 8 -0.05 -0.10 -0.15

Explanation / Answer

wave equation

y = A*cos(kx + wt+phi)

amplitude A = 0.1 m

wavelength lambda = 4 m

time period T = 10/5 = 2 s

w = 2pi/T = 2*pi/2 = pi rad/s

k = 2pi/lambda = pi/2

for particle x = 0 , at t = 3

y = -0.1

-0.1 = 4*cos((pi*3)+phi)

phi = -7.83

wave equation

D(x,t) = 4*cos( (pi/2)x + pit - 7.83 )

(b)

speed = v = w/k = 2 m/s

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