Wolfram Demonstrations Project: "Superposition of Waves"

To use this demonstration, you must download and install the Mathematica Viewer from the Wolfram Demonstrations Project. This demonstration illustrates the superposition of two waves traveling in opposite directions. First, try setting the frequencies of the two waves to be equal. Notice that as the time passes, the superposition of two waves goes from “double” the wave (the wave with the same frequency and twice the amplitude), when the waves are in same phase, to “no wave” (the waves cancel each other out completely), when they are in the opposite phase. Then, explore what happens when the frequencies of the waves are close to each other, but a little bit different. How does the superimposed wave look like? This effect is easier to see when the frequencies are large. Try clicking on the “plus” icon in the top right corner of the demonstration, and selecting “autorun.” Notice that the superimposed wave contains an oscillation within an oscillation, one with the sum, and another one with the difference of the original frequencies.