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Understanding wave properties includes developing a mathematical relationship for a traveling wave. Shown in black is a traveling wave (position is given in centimeters and time is given in seconds).  Measure the relevant properties of this wave and determine the wave function of the wave. Once you are finished, check your answer by entering a function, f(x, t), in the text box and looking at the red wave to see if it matches.  Restart.

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With an understanding of the mathematical description of a traveling wave, we can now explore what happens when traveling waves run into each other:  the superposition of waves.  Restart.  A superposition of two traveling waves is nothing more than the arithmetic sum of the amplitudes of the two underlying waves. We represent the amplitude of a transverse wave by a wave function, y(x, t).  Notice that the amplitude, the maximum value of y, is a function of position on the x axis and the time. Given two waves moving in the same medium, we call them y₁ = f(x, t) and y₂ = g(x, t). Their superposition, arithmetic sum, is written as f(x, t) + g(x, t). This may seem like a complicated process, but we simply need to add the waves together at each point on the string (position is given in centimeters and time is given in seconds).  Consider the two waves shown above. If these two wave packets are traveling on the same string, draw on a piece of paper the superposition of the two wave packets between t = 0 and t = 20 s in 2-s intervals for each animation.

When you have completed the exercise, check your answers with the animations provided below.

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