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7Creview - SHM Wave basics Interference Interference...

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SHM Wave basics Interference Interference summary Standing waves Ray optics Ray optics summary Thin lenses Thin lens summary Gravity Gravitational field Gravitational force Acceleration due to gravity Gravitational potential energy Electrostatics Fields and forces Potential and potential energy Field lines Equipotentials Dipoles Magnetostatics Fields and forces Magnetic field line Right Hand Rule #1 Right Hand Rule #2 Dipoles Induction Electromagnetism Polarization Quantum mechanics De Broglie wavelength Particle in a box Harmonic oscillator Photons Hydrogen atom Line spectra Pauli exclusion principle 1 Saturday, 13 March 2010
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Conditions for SHM * Must have an equilibrium * Must have a restoring force when displaced from equilibrium * Force must take the form Simple Harmonic Motion (SHM) m Equilibrium Equilibrium F = ma = k ( y y 0 ) where y 0 is equilibrium y is the current position k is a constant characteristic of the system. For a mass spring system k is the spring constant, for a pendulum k = mg/L y-y0 y-y0 y-y0 y ( t ) = A sin 2 π T t + φ 0 + y 0 A “amplitude”: max. displacement t “time” φ 0 “fixed phase”: tells us about initial conditions T “period”: time to repeat Motion described by f = 1 2 π k m , T = 1 f = 2 π m k indep of A, phi 0 TOC 2 Saturday, 13 March 2010
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Wave basics TOC y ( x, t = 3 s ) λ Amplitude To describe a wave we need An amplitude A A period T A fixed phase constant φ 0 A direction ( ± ) A wavelength λ A wave speed v = λ f = λ /T x (m) t (s) y ( x = 1 . 5 m, t ) period period WRONG!!! y ( x, t ) = A sin( Φ ( x, t )) + y 0 where Φ ( x, t ) = 2 π T t ± 2 π λ x + φ 0 Note: pick x constant – then you just have SHM with “constant phase” φ 0 ± 2 π λ x Amplitude This case: y ( x, t ) = (3 m ) sin 2 π 6 s t + 2 π 4 m x + π 4 See if you can show it from the graphs! 3 Saturday, 13 March 2010
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Waves-Interference TOC Source 1 Source 2 d x 1 x 2 x point of interest General goal: Figure out if the interference will be constructive, destructive or partial at the “point of interest”. Strategy: Look at the di ff erence in total phase ∆Φ = Φ 2 Φ 1 . We have three cases: ∆Φ = (even) π – constructive ∆Φ = (odd) π – destructive ∆Φ = (integer) π – partial Tool: Phase chart, which lists all sources of total phase.
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