Two graphs depict a one-dimensional water wave, as a function of time, for two s

Question

Two graphs depict a one-dimensional water wave, as a function of time, for two separate positions. The top graph represents x = 1.0 m and the bottom graph represents x = 1.1 m. a) Provide a detailed description of how you know which direction the wave is traveling. This includes a careful description of what the graphs represent. Also, be prepared to describe what assumption(s) you are making in order to answer the questions. (Comment: Once you can make clear, well-thought descriptions for the above, you can feel comfortable that you have a pretty good understanding of the graphical representation of 1-D simple harmonic waves.) b) Write an equation of the motion y(x, t) for this wave. Specify values of A, T, lambda, and phi.

Explanation / Answer

A) at t =0, y is maximum at x=1.1 and little lesser at x=1

At t=0.20, y is maximum at x=1 and little lesser at x=1.2

It is travelling in negative x direction because we can see that just after x= 1.1 had maximum y value, x=1.0 had its maximum y value.

B) y = A sin( kx + wt + phi)

Here amplitude A= 0.1,

Time period T=1.6s

w = 2pi/T = 2pi/1.6 = 3.93 rad/s

Speed v = (1.1-1)/0.2 = 0.5 m/s

lambda = v/f = v*T = 0.8 m

k = 1/lambda = 1.25 per m

Putting the values,

0.1 = 0.1 sin (1.25*1.1+3.93*0+phi)

Here 1.25*1.1 + phi = pi/2

phi = pi/2 - 1.25*1.1

= 0.196 radians

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