Physics Lecture 9

Physics Lecture 9 - = -25cos(10x-5t = v max = abs(f(x)) =...

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Lecture 9: Traveling Waves I. Properties of traveling waves 1. Wave N coupled oscillators in limit N huge 2. Traveling Wave – wave that propagates 3. Longitudinal - ||||||||||||||||||||| v 1. pieces oscillate parallel to the propagation 4. transverse – pieces oscillate perpendicular to the propagation 5. lambda = wavelength A = amplitude – distance from axis to max or min 6. follow a point where y = 0 => kx +/- ωt = 0 1. x = (ω/k)t 2. abs(ω/k) = v prop 7. Direction: if kx is in the plus or minus i hat directon, if ky is in the plus or minus j hat 1. if ω and k are same sign negative direction 2. if ω and ka re the opposite sign positive direction 1. ex y = 5sin(25t+15z) v prop -k(hat) 2. sound wave has a frequency of 2000hz what is λ 1. v sound = 340 m/s v = λ (f) v/f = 340/2000 = λ= .17 3. propagation speed is a property of the wave so if frequency changes the velocity will not necessarily 4. two velocities 1. propagation – speed wave motion 2. v of particles in wave 3. v – dy/dt for string 5. v prop = dy/dt = 5cos(kx-5t)(-5)
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Unformatted text preview: = -25cos(10x-5t = v max = abs(f(x)) = 25m/s II. Doppler Effect 1. received frequency 1. received ~ source +/- Δ(f) 2. approx: Δ(f)/source frequency ~ u/v 1. u: relative velocity of source/receiver 2. v: propagation speed of the wave 3. Δ(f) is positive if waves are approaching Δ(f) is negative if the waves are receding 4. if approaching: source + your velocity(source)/c 5. concept test 1. detected frequency = f you + speed of the car/c(f you) detected frequency = f you + speed of the car/c(f you) + speed of the car/c(f you) detected frequency = f you + 2*speed of the car/c(f you) 2. FM Waves 1. harmonic FM waves 1. E(x,t) = E m sin(kx +ω (t)) B(x,t) = B m sin(kx +ω (t)) 2. E = Bc E m = B m c 3. right hand rule E x B: fingers to E rotate to B y(x,t) = Asin(kx +/- omega(t)) A = Amplitude k = 2π/λ= wave number ω= 2 π f = 2π/T = angular frequency f = 1/T V prop = λ (f) = ω/k Doppler Shift: f R = f S +/- Δ(f)ω Δ(f)/ f S ~ u/v if u<<v...
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This note was uploaded on 04/07/2008 for the course PHYS 212 taught by Professor Ladd during the Spring '08 term at Bucknell.

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