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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 y1(x, t) and y2(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