WAVE EQUATION

This Mathlet illustrates the solution to the wave equation representing a frictionless plucked string.

A large graphing window displays the initial condition -- the string of the string at $$t = 0$$ -- with a thin yellow polygon, and the plucked point with a diamond.

Toggles below the large graphing window control what else is displayed. Selecting [Solution] shows the solution as a yellow polygon. [Harmonics] toggles display of some of the Fourier components of the solution, in white. A slider at bottom selects the number of harmonics. [Fourier sum] toggles display, in cyan, of the sum of the selected number of harmonics. [Left wave] creates the left-moving traveling wave in the d'Alembert solution, in green, and [Right wave] creates the right-moving traveling wave, in orange.

Grabbing the handle on the time slider selects the time. The display can also be animated using the [>>] key at left. Once the animation has started, the key is replaced by [||], and selecting it stops the animation. The speed of the animation is controlled by a slider marked [Animation speed].

Rolling over the graphing window produces crosshairs and a readout of the values of $$x$$ and $$u$$. Depressing the mousekey suppresses the crosshairs and repositions the pluck point to the nearest possible point (since it is constrained by $$0 \leq x \leq 1$$).

© 2013 H. Miller, J. Orloff, and J.-M. Claus