4 Vibration Spectrum of One-Dimensional Waves

Modern Physics

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PHY251 - Waves on a string PHY 251 Vibration Spectrum of 1-Dimensional Waves Introduction In this experiment we study standing waves on a long rubber band stretched between fixed supports. These standing waves are analogous to the wave functions of a particle in an infinitely deep potential well. If one end of a long rubber band is subjected to forced periodic vibrations, traveling waves will propagate down the rubber band with velocity v = ( T / μ ) (1) where T is the tension in the band and μ is the mass per unit (stretched) length of the rubber band. The wavelength λ is related to the frequency ν of the driving force and the velocity of propagation v as λ = v / ν . Waves reflecting off the far end of the rubber band interfere with incident waves, and for certain driving frequencies a stable pattern emerges, with fixed points of destructive interference (nodes) and constructive interference (anti-nodes). If the rubber band is very long, the wave is dissipated by friction before it reaches the far end, and no interference occurs. If this is not the case, then the wave can reflect
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