To obtain insight into the more precise behavior of a plucked vibrating string, it is helpful to consider the traveling wave-based theory of plucked string vibrations. Imagine an infinitely long stretched string that is plucked simultaneously at three points to create an initial triangular displacement, as shown by the thick black line in the initial state of the plucked string animation. Press the ``play'' button of the Flash animation, and watch what happens when the ``three picks'' are released. The thick black line shows what happens to the ideal string. The corners at first flatten, and then two half-amplitude triangular pulses emerge, traveling in opposite directions. These are traveling waves. In fact, the initial shape of the string is best considered as the sum of those two half-amplitude pulses. When one of these traveling waves encounters the end of the string, it reflects back in the other direction. For more information, see the traveling waves laboratory assignment. For a mathematical derivation of this classical traveling-wave model for ideal plucked-string behavior, see the page entitled ``Elementary String Instruments'' in the online textbook Physical Audio Signal Processing.
