PHY183-Lecture50 - Few points ! SOCT (Student Opinion of...

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Unformatted text preview: Few points ! SOCT (Student Opinion of Courses and Teaching) Online Forms: PHY 183 4/17/2006 5/12/2006 http://rateyourclass.msu.edu ! Final Exam date: Thurs. May 4, 8-10 pm E100 VMC (Veterinary Medical Center) Bldg. Physics for Scientists & Engineers 1 Spring Semester 2006 Lecture 50 April 21, 2006 Physics for Scientists&Engineers 1 1 April 21, 2006 Physics for Scientists&Engineers 1 2 Waves ! Oscillating excitations that propagate through space as a function of time Waves transport energy across spatial distances BUT usually do not transport matter with them Oscillations - Review (1) ! Simple harmonic motion ! ! " A series of oscillators coupled to their nearest neighbors ! The oscillation propagates, not the oscillators ! More abstract concept ! Waves can interfere with each other => Interference patterns Equation of motion Solution F = !kx # d2x k + x=0 dt 2 m x(t ) = A sin (!0t + " 0 ) Physics for Scientists&Engineers 1 !0 = k m 4 April 21, 2006 Physics for Scientists&Engineers 1 3 April 21, 2006 Oscillations - Review (2) ! Period Review: Damped Oscillations 1 f = T Introduce damping force into our equations of motion: 2! T= "0 Frequency: Fd = !bv m d 2x dx = !b ! kx 2 dt dt d 2 x b dx k + + x=0 dt 2 m dt m Small damping: Large damping: Critical damping: April 21, 2006 Physics for Scientists&Engineers 1 5 April 21, 2006 b < 4mk b > 4mk b = 4mk Physics for Scientists&Engineers 1 6 Quiz 50.1 ! In the figure below, list the curves in order from smallest to largest damping constant b? A) Green, Blue, Red B) Green, Red, Blue C) Red, Blue, Green D) Red, Green, Blue E) Blue, Green, Red Experiment ! Video sequence with "t=0.133 s between two frames ! Push first rod ! Pulse moves down the line ! Constant velocity April 21, 2006 Physics for Scientists&Engineers 1 7 April 21, 2006 Physics for Scientists&Engineers 1 8 Waves ! Throw a stone in water and watch circular wave crests travel outward Ripples move outward in concentric circles Object swimming on the surface stay in place, apart from some up-and-down motion as the wave crests move through under the object "The Wave" - "La Ola" ! 3 types of waves: Mechanical: water, sound, seismic... material medium required Electromagnetic: radio, microwaves, X rays etc... no material medium required Matter: quantum physics... April 21, 2006 Physics for Scientists&Engineers 1 9 April 21, 2006 Physics for Scientists&Engineers 1 10 "The Wave" - "La Ola" ! How fast does the wave travel around the stadium? ! Answer: People jump up when they see their neighbor jump up Reaction time delay ~ 0.1 s Spacing of seats ~ 2 feet ~ 0.6 m Wave moves 0.6 m in 0.1 s: v = (0.6 m)/(0.1 s) = 6 m/s Periodic Sinusoidal Pulses ! So far we only looked at a single wave pulse ! Now use periodic sinusoidal excitation with frequency f = 1/T. ! Again excitation will travel with a constant speed ! In our chain of coupled oscillators, we observe a sinusoidal motion moving down the chain ! Distance in space between two consecutive maxima is called wavelength, !. ! During one period, wave front advances by one wavelength ! Wave speed ! ! Empirically found: v ~ 12 m/s (people anticipate arrival of wave) Interesting (perhaps...) side note: there is even a temperature dependence of the speed of the wave (University of Nebraska research) v= T " v= !f April 21, 2006 Physics for Scientists&Engineers 1 11 April 21, 2006 Physics for Scientists&Engineers 1 12 Transverse and Longitudinal Waves ! Transverse Waves: Oscillators move perpendicular to direction of wave propagation ! Suppose member of chain at x=0 oscillates with Mathematical Description of Waves y ( x = 0, t ) = A sin(!t + "0 ) ! Time delay for the oscillation to move distance x is Example: Light waves !t = x v x y ( x, t ) ! y (0, t " ) v ! Longitudinal wave: Oscillators move back and forth in the same direction the wave propagates ! Then we can write for the wave y (x,t): Example: Sound waves April 21, 2006 Physics for Scientists&Engineers 1 13 April 21, 2006 x # # x$ $ y ( x, t ) = y (0, t % ) = A sin & ! & t % ' + "0 ' v ( ( v) ) Physics for Scientists&Engineers 1 14 Wave Number ! Using f = 1/T and v = !f, we obtain: Wave Number and wave function ! Defining the wave number: ! = Note the similarity with 2" # x& # & # y(x,t) = Asin % 2! f % t " ( + )0 ( $ $ ' v' $ % x = A sin ' 2! ft & 2! f + "0 ( #f ) * % 2! t 2! x ( = Asin ' " + $0 * & T ) # 2" != # "= 2! T ! The wave function reads: ! Definition of wave number: ! Wave equation: y(x,t) = Asin (! t " # x + $0 ) ! One can check that: y(x,t) = Asin (! t " # x + $0 ) April 21, 2006 Physics for Scientists&Engineers 1 15 April 21, 2006 y ( x, t + T ) = y ( x, t ) y ( x + ! , t ) = y ( x, t ) Physics for Scientists&Engineers 1 16 ...
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This note was uploaded on 03/19/2008 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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