Class13 - Standing Waves The other really useful...

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2/6/12 Oregon State University PH 202, Lecture 13 1 Standing Waves The other really useful application of wave interference is the standing wave. For example, most musical instruments rely on this phenomenon. They use standing waves of sound to generate musical tones of very reliable frequency (pitch). How? A standing wave occurs when many waves overlap due to reflections of the same disturbance in the same available space. The interfer- ence of all these reflected waves tend to cancel each other out except for waves that “fit the available space.” The reflections that don’t cancel each other out are those that are completing a cycle or half-cycle when they encounter the end of the available space. They reflect back in a “harmonized” way, thus reinforcing each other (i.e. forming constructive interference), increasing the amplitude of their sum. We hear this as resonance .
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2/6/12 Oregon State University PH 202, Lecture 13 2 How does the end of the available space govern the standing wave? It fixes the value of the wave function. For example, a guitar string is fixed at both ends. Its function (a transverse displacement) is thus forced to be zero at each end. We call such zero displacement a node in the standing wave. The guitar string is a good example of a transverse standing wave. What about a longitudinal standing wave—such as sound?
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2/6/12 Oregon State University PH 202, Lecture 13 3 In a longitudinal pressure wave (sound), the air particles are being displaced back and forth (along the axis of the wave travel)—and they are undergoing pressure variations, too. Both of these—displacement and pressure—vary sinusoidally, but it
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This note was uploaded on 03/10/2012 for the course PH 202 taught by Professor Staff during the Winter '08 term at Oregon State.

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Class13 - Standing Waves The other really useful...

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