Chapter_15 - 5 Superposition and Interference 1 t x D 2 t x D k f v λ= = Ch 15 Wave Motion 6 Power P and Intensity I 2 M D P ∝ Power scales as

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Ch 15: Wave Motion Focus: Wave Basics ) v ( ) , ( t x f t x D = l 1) Wavelength l = spatial period Transverse wave: displacement perpendicular to propagation direction (like a string or rope) µ T = v 2) Wave velocity v for a String , tension T(N), mass/length m( kg/m ) 3) Wave Motion D(x,t = 1 s) x (m) v 3 2 ) 3 ( 1 5 ) , ( t x t x D + = Example: v = ? D = displacement Longitudinal wave: displacement parallel to propagation direction (compression wave, like sound) - moves right , + moves left
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Ch 15: Wave Motion 4) Sinusoidal travelling wave = ) v ( 2 sin ) , ( t x D t x D M λ π D M = maximum displacement = amplitude = T t x D t x D M 2 2 sin ) , ( Sine oscillates in space and time, so write in terms of period T and wavelength l : T = v T ω 2 = angular frequency w 2 = k angular wavenumber k T f 1 = frequency f in cycles per second (Hz) () t x k D t x D M = sin ) , ( or WHY (physically) is this the velocity? ) , ( ) , ( ) , ( 2 1 t x D t x D t x D + = Amplitudes add —what happens when they meet?
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Unformatted text preview: 5) Superposition and Interference ) , ( 1 t x D ) , ( 2 t x D k f / v λ= = Ch 15: Wave Motion 6) Power P and Intensity I ( ) 2 M D P ∝ Power scales as square of maximum displacement—like spring and kinetic energy: A 1 (area in) A 2 (area out) I 1 I 2 P P Power in = power out: 2 2 1 1 A I A I = Intensity I is power/area = P/A 2 2 2 2 1 1 r I r I = Example: Spherical wave: A = 4 p r 2 r 2 r 1 7) Standing Waves and Resonance String: length L l 1 /2 = L 2(l 2 /2) = L Nodes at ends integer ,... 2 , 1 n / 2 = = n L n λ Integer number of half waves fit: l fundamenta ) 2 /( v f 1 L = 1 f n / v = = n n f (n th overtone) Add a node: Draw Pictures!...
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This note was uploaded on 05/13/2010 for the course PHYSICS 53L taught by Professor Mueller during the Fall '07 term at Duke.

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Chapter_15 - 5 Superposition and Interference 1 t x D 2 t x D k f v λ= = Ch 15 Wave Motion 6 Power P and Intensity I 2 M D P ∝ Power scales as

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