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Converted document Traveling Wave Demo

Traveling Wave Demo

After seeing the unforced vibrating string, we look at the travelling wave solution. A solution to this problem is given as
(1) ν(x, t) = (1)/(2)∞⎲⎳i = 1Fi⎧⎩sin⎡⎣(iπ)/(ℓ)(x + √((T)/(m))t)⎤⎦ + sin⎡⎣(iπ)/(ℓ)(x − √((T)/(m))t)⎤⎦⎫⎭
Where
(2) Fi = (2)/(ℓ)ℓ⌠⌡0f(x)sin⎛⎝(iπx)/(ℓ)⎞⎠ dx
and f(x) describes the initial shape of the string. For this case, the initial shape of the string can be seen by setting the time to 0. Once this is done, there are two lines visible: a solid line and a dashed line. The dashed line is actually two lines on top of one another, and the solid line is the sum of these. These dashed lines represent the two sin terms in the equation, and the solid line represents the full solution. Increase the mode shapes, and press play on the time slider bar to see how the three lines correspond to one another. Press the slower button if the simulation is too fast.