Standing Waves

As the adjacent section moves upward it begins to

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Unformatted text preview: the adjacent section moves upward, it begins to pull the next section upward, and so on. Meanwhile, you pul down on your end of the string. As each section moves upward in turn, it begins to be pulled back downward by neighboring sections that are already on the way down. The net result is that a distortion in the string’s shape (the pulse) moves along the string at some velocity v. If you move your hand up and down in a continuous simple harmonic motion, a continuous waves travels along the string at velocity v. Because the motion of your hand is a sinusoidal function of 1 time, the wave has a sinusoidal shape at any given instant, that is, the wave has the shape of a sine curve or a cosine curve. First, we consider here only an “ideal” string, in which no friction-like forces within the string causes the wave to die out as it travels along the string. In addiction, we assume that the string is so long that we need not consider a wave rebounding from the far end. One way to study these waves is to monitor the wave forms (shapes of the waves) as they move to the right. Alternatively, we could monitor the motion of an element of the sting as the element oscillates up and down while a wave passes through it. We could find that the displacement of every such oscillating string is perpendicular to the direction of travel of the wave. This motion is said to be transverse, and the wave is said to be a transverse wave. Now consider the case of a sound wave being produced by a piston in a long, air-filled pipe. If you suddenly move the piston rightward and then leftward, you can send a pulse of sound along the pipe. The rightward motion of the piston moves the elements of air next to it rightward, changing the air pressure there. The increased air pressure then pushes rightward on the elements of air somewhat farther along the pipe. Moving the piston leftward reduces the air pressure next to it. Thus, the motion of the air and the change in air pressure travel rightward along the pipe as a pulse. If you push and pull on the piston in simple harmonic motion a sinusoidal wave travels along the pipe. Because the motion of the elements of air is parallel to the direction of the wave’s travel, the motion is said to be longitudinal, and the wave is said to be a longitudinal wave. Both a transverse wave and a longitudinal wave are said to be traveling waves because they both travel from one point to another, as from one end of the string to the other end. Note that it is the wave that moves from end to end, not the material (string or air) through which the wave moves. 2.3 Waves on a String The prototype of a one-dimensional wave is a wave on a...
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This document was uploaded on 03/20/2014 for the course PHYS 215 at Lafayette.

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