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One of the most interesting phenomena we can explore is that of a superposition of waves. Restart.
A superposition of two waves is nothing more than the arithmetic sum of the amplitudes of the two underlying waves. We can represent the amplitude of a transverse wave by a wave function, y(x, t). Notice that the amplitude, the value y, is a function of position on the x axis and the time. If we have two waves moving in the same medium, we call them y_{1}(x, t) and y_{2}(x, t), or in the case of this animation, f(x, t) and g(x, t). Their superposition, arithmetic sum, is written as f(x, t) + g(x, t).
This may seem like a complicated process, so we often focus on the amplitude at one point on the x axis, say x = 0 m (position is given in meters and time is given in seconds). So now let's consider Animation 1, which represents waves traveling on a string. The top panel represents the right-moving Gaussian pulse f(x, t), the middle panel represents g(x, t), the left-moving Gaussian pulse, and the bottom panel represents what you would actually see: the superposition of f(x, t) and g(x, t).
As you play the animation focus on x = 0 m. Until the tail of each wave arrives at x = 0 m, the amplitude there is zero. What happens during the time that the two waves overlap?
What does the superposition in Animation 2 look like at t = 10 s? Explain.
What about at a later time?
Original problem: Illustration 17.3, Physlet Physics
by Christian and Belloni
© 2004 by Prentice-Hall, Inc. A Pearson Company