lecture25-musical instruments and standing waves-

# lecture25-musical instruments and standing waves- - What...

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What you will be able to do a/er today … how (and where) an5-nodes and nodes are formed for a pressure wave explain how this relates to the displacement standing wave Explain … the frequency of various harmonics in a closed- closed, open-open, and open-closed system Calculate … your understanding of pressure change (Bernoulli) to standing waves Apply …

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Mathematics of a Standing Wave • Superposition of a wave and its own reflected wave: Frequencies and amplitudes are equal. D 1 ( x , t ) = D M sin( kx ! ! t ) D 2 ( x , t ) = D M sin( kx + t ) D = D 1 + D 2 = D M sin( kx ! t ) + sin( kx + t ) [ ] D = 2 D M sin( kx )cos( t ) amplitude simple harmonic motion (think spring) D = A ( x t )
Wed worksheet: 2f • What is the AMPLITUDE of a point located at x = 0.12 cm? amplitude A ( x ) = (8 cm )sin(3 x ) A ( x = 0.12 cm ) = (8 cm )sin(3 ! 0.12 cm ) A = 2.82 cm D 1 ( x , t ) = 4 cm sin(3 x ! 2 t ) D 2 ( x , t ) = 4 cm sin(3 x + 2 t ) D 1 + 2 ( x , t ) = 8 cm sin(3 x )cos(2 t )

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Standing Waves, Resonance Wave interfering with its own reflected wave. If the frequency is b just right ` , constructive and destructive interference will lead to a wave pattern that is fixed in space = standing wave . – standing wave moves up and down, NOT left to right Certain wavelengths will fit inside a given L. Thus certain frequencies are allowed à these are called the resonant frequencies of the object (strings, open or closed tubes, boxes. ..).
Standing Wave: string instruments (closed-closed) !

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## This note was uploaded on 01/15/2012 for the course PHYS 101 taught by Professor Bates during the Winter '08 term at The University of British Columbia.

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lecture25-musical instruments and standing waves- - What...

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