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Ocean waves with a crest to crest distance of $10$ meters can be described by the wave function $$y=(0.8\text{ meters})\sin[0.628(x-vt)]$$ where $v=1.2 \text{ meters/s}$.

a) Sketch $y$ at $t=0$.
b) Sketch $y$ at 2 seconds.

I believe this to have been in some way derived from the equation $y = A \sin (\omega t + kx)$ where 0.8 is the amplitude of the wave.

I don't understand what the $x$ in this questions comes from. Any clues?

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andy07070
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1 Answers1

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$x$ is horizontal distance in the direction the wave is traveling. $y$ is vertical displacement of the surface. At a given $t$ you now have an equation $y=f(x)$ which you are being asked to graph. You are correct that it will be a sine wave of amplitude ($0$ to peak) $0.8$ meters. The change in $t$ will offset the origin of the sine wave.

Ross Millikan
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  • So x is the movement of the wave on the horizontal axis, ok i understand that. What i cant understand is to plot y at 2 seconds the value of x at 2 seconds will need to be known, i have no idea how to find that. – andy07070 Apr 15 '13 at 17:19
  • At 2 seconds y=0.8sin(0.628*(x-2.4) – andy07070 Apr 15 '13 at 17:21
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    @andy07070: that is correct. Now just pick a number of points $x_i$ calculate $y_i$ from your equation, and plot them. I would suggest a range of $x$ from $0$ through $10$. Do this for each of the two equations. They should look the same except one is shifted horizontally from the other by $2.4$ – Ross Millikan Apr 15 '13 at 17:23
  • ahhhh of course, so foolish. thanks – andy07070 Apr 15 '13 at 17:24