# lecture31 - Standing Waves Text sections 18.2-18.4 18.2...

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Text sections 18.2 Text sections 18.2 -18.4 18.4 Standing Waves Practice: Chapter 18, problems 13, 15, 17, 25, 49 Practical Setup : Fix the ends, use reflections. µ λ T F v f = = node node L L v f L L 2 2 1 1 1 2 1 = = = (“fundamental mode”) We can think of travelling waves reflecting back and forth from the boundaries, and creating a standing wave. The resulting standing wave must have a node at each fixed end. Only certain wavelengths can meet this condition, so only certain particular frequencies of standing wave will be possible. example:

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λ 2 1 2 2 2 f L v f L = = = λ Second Harmonic λ 3 1 3 3 3 2 3 3 2 3 3 2 3 f L v v f L L = = = = = Third Harmonic . . . . In this case (a one-dimensional wave, on a string with both ends fixed) the possible standing-wave frequencies are multiples of the fundamental: f 1 , 2f 1 , 3f 2 , etc. This pattern of frequencies depends on the shape of the medium, and the nature of the boundary (fixed end or free end, etc.).
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lecture31 - Standing Waves Text sections 18.2-18.4 18.2...

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