[url=http://mathlets.org/mathlets/wave-equation/]http://mathlets.org/mathlets/wave-equation/[br][/url][br]The "left wave" and the "right wave" in the applet are exactly [math]\frac{1}{2}f^{\ast}\left(x-ct\right)[/math] and [math]\frac{1}{2}f^{\ast}\left(x+ct\right)[/math] that appear in Remark 4.8.[br][br]Another interesting thing is the see how the "harmonics" (i.e. the Fourier coefficients) change when you "pluck" the string on the side or in the middle.