p140w07_ct_24 - Physics 140: Winter 2007 Lecture #23 April...

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Unformatted text preview: Physics 140: Winter 2007 Lecture #23 April 10, 2007 Dave Winn Racquetball Striking a Wall Copyright: Loren M. Winters Mt. Etna Andrew Davidhazy Predicting the speed of waves Speed must be set by some combination of coupling between oscillators and inertia Waves on a string: tension vs. linear density v = (T / ) Sound waves: compressibility vs. density v = (B / ) Usually: frequency of waves determined by an outside disturbance (like me) Wavelength is then determined by how fast waves run away from the point of disturbance: fast waves => large The speed of waves on a string is set by the tension and the mass per unit length. I send waves of frequency f down the string which is under tension T , I get waves with wavelength . What happens if I double the tension; how does the wavelength change? 1: < 2: = 3: > Disturbances of all kinds take time to travel. When I release this slinky, it takes time for the release of the end to travel to the bottom. As a result, the slinky all gathers together first, then falls to the floor Mathematical description of waves Consider a sinusoidal wave Wave peaks are when Written in a slightly different way: Peaks move to the left ( ) f 2 2 sin ) , ( = = = k t kx A t x y f k v t k x t kx = = + = = 2 or 2 Positive v, travels to the right ( ) t kx A t x y + = sin ) , ( k t k x t kx 2 2 + = = + Negative v, travels to the left An example Consider this wave Wavelength Frequency Wave speed ( ) t x t x y 5 . 4 . 3 sin . 4 ) , ( + = . 3 2 . 3 2 = = = k 2 5 . 4 5 . 4 2 = =...
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This note was uploaded on 04/04/2008 for the course PHYSICS 140 taught by Professor Evrard during the Fall '07 term at University of Michigan.

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p140w07_ct_24 - Physics 140: Winter 2007 Lecture #23 April...

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