Assignment_5_08

Assignment_5_08 - TA's Name Section Your Name Physics 214...

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TA's Name:____________________ Section: ____ Your Name: _________________________________ Physics 214 Assignment 5 Concepts: Boundary conditions Fourier analysis Reflection and Transmission of waves Superposition Reading: AG Notes on Superposition and Standing Waves (from website); Y&F, Vol. 1, Chapter 16 Assignment: Due in lecture on Tuesday, February 26. Please turn in this sheet stapled to the top of your work. 1. (a) Consider standing waves on a string of length L that is fixed at both ends. How far are (i) the first node and (ii) the first antinode from the fixed end? (b) Now consider a string of length L that has one fixed end and one ideal free end (implmented using a massless slip ring.) How far are (i) the first node and (ii) the first antinode from the fixed end? (c) It's very hard to make an ideal free end. But fixed ends are easy. Using some extra rope and a fixed end, how might you create the standing wave pattern you'd get from a rope of length L with one free end? 2. At t = 0, the wave pulses shown below are moving away from one another. The wave speed is 5 m/s. The left end ( x = 0) is free (massless slip-ring boundary condition) and the right end ( x = 25 m) is fixed. 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 x (m) y (cm) Free End (a) Draw the left end of the string (0 x 4 m) at t = 1.2 s. (b) Draw the right end of the string (21 m x 25 m) at t = 2.0 s. (c) Draw the velocity distribution (a graph of / yt as a function of x ) at t = 4.2 s for the part of the string where the velocity is nonzero. Physics 214, Spring 2008 1 Cornell University
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Physics 214, Spring 2008 2 Cornell University 3. A sound tube has an end at x = 0. An incident wave s i = s m cos ( kx + &t ) is reflected from x = 0 with amplitude Rs m , where R is called the reflection coefficient and is in the range –1 R 1. The resulting displacement of a fluid element is given by s ( x , t ) = s m cos ( kx + ω t ) + Rs m cos ( kx t ) (a) What value of R
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This note was uploaded on 04/03/2008 for the course PHYS 214 taught by Professor Thorne during the Spring '08 term at Cornell.

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Assignment_5_08 - TA's Name Section Your Name Physics 214...

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