Assignment_5 spring 2012

# Assignment_5 spring 2012 - TA's Name Section Your Name...

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Physics 2214 Assignment 5 Concepts: Wave reflection and transmission Dispersion relations Characteristic impedance Group velocity impedance matching Wave Interference II: Beats Reading: Lecture notes 8, 9 and 10; Y&F, Vol. 1, Chapters 15 and 16; Assignment: Due in homework boxes opposite 125 Clark Hall before 430 pm on Tuesday February 28. Recommended coops: Problems 1,5 and 6. Please turn in this sheet stapled to the top of your work. Physics Problems: 1. Boundary conditions. At t = 0, the wave pulses shown below are moving away from one another. The wave speed is 4 m/s. The left end ( x = 0) is free (massless slip-ring boundary condition) and the right end ( x = 25 m) is fixed. (a) Draw the left end of the string (0 x 4 m) at t = 1.5 s. (b) Draw the right end of the string (21 m x 25 m) at t = 2.5 s. (c) Draw the velocity distribution (a graph of as a function of x ) at t = 5 s for the part of the string where the velocity is nonzero. 2. Wave transmission across a boundary. String 1 with wave speed v 1 is connected to string 2 with wave speed v 2 . A square pulse of width W is incident from string 1 onto the boundary between strings. TA's Name:____________________ Section: ____ Your Name: _________________________________ Physics 2214, Spring 2012 1 Cornell University

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(a) Sketch the reflection coefficient R and transmission coefficient T for this pulse as a function of the ratio v 2 /v 1 . Label important magnitudes. (b) Can the transmitted wave amplitude be larger than the incident amplitude? If so, when, and why? (c) Can the reflected wave amplitude be larger than the incident amplitude? If so, when and why? (d) You notice that the transmitted pulse appears to be roughly half as wide as the incident pulse. Will the reflected pulse have the same sign or be inverted relative to the incident pulse? (e) Is wave reflection symmetric? How does the reflection coefficient for waves incident upon string 2 from string 1 compare with that for waves incident from string 1 from string 2, for the general case v 1 v 2 ? Express your answer as a ratio.
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Assignment_5 spring 2012 - TA's Name Section Your Name...

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