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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 / λ ) • Sound waves: compressibility vs. density v = √ (B / ρ ) • 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 λ 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 λ . What happens if I double the tension; how does the wavelength change? 1: λ < λ 2: λ = λ 3: λ > λ 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 ) , ( π ω λ π ω = = − = k t kx A t x y f k v t k x t kx λ ω π ω π ω = = + = = − 2 or 2 Positive v, travels to the right… ( ) t kx A t x y ω + = sin ) , ( k t k x t kx 2 2 π ω π ω + − = = + 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 − = − = = π λ λ π k π π ω 2 5 . 4 5 . 4 2 = =...
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 Fall '07
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 Physics, racquetball, Mt. Etna, Andrew Davidhazy, Loren M. Winters

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