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Assignment 7 spring 2012

Assignment 7 spring 2012 - TA's Name_Section Your Name...

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Physics 2214 Assignment 7 Concepts: Energy and power in waves Electromagnetic waves Fourier analysis, non-sinusoidal drives Plane waves Maxwell equations in differential form Relation between E, B and v Reading: Lecture Notes 10, 11, 12 and 13; Y&F, Vol. 1, Chapter 15 and 16, Vol. 2 Chapter 32, 33. Assignment: Due in homework boxes opposite 125 Clark Hall before 430 pm on Tuesday, March 13. Recommended coops: Problems 3,4 and 7 Please turn in this sheet stapled to the top of your work. 1. Energy in wave motion. String 1 of mass density 1 kg/m is connected to string 2 of mass density 0.01 kg/m at x=0. The tension in the strings is 100 N. At t=0, a symmetric trapezoidal pulse of y height 1 cm and base widths 0.5 m and 1 m is launched from string 1 toward string 2. The leading edge of the pulse at t=0 is at x=-10 m. (a) Sketch the y displacement of the strings versus position at (i) t=0 and (ii) t = 2 s. Give numeric values for all positions, heights and widths. (Graph paper might help.) (b) Graph the kinetic energy density as a function of x at (i) t=0 s and (ii) t=2 s. (c) Graph the potential energy density as a function of x at (i) t=0 s and (ii) t=2 s. (d) What are the total kinetic energy and the total potential energy at (i) t=0 s and (ii) t=2 s? (e) What is the total energy of the string at (i) t=0 s and (ii) t=2 s? Is energy conserved? 2. Superposition and Energy. Consider two triangular pulses of width W and height +A, which are launched from opposite ends of a string toward each other. The string tension is τ and mass per unit length is μ . (a) What is the total energy of each pulse? What is the total energy of the string when the pulses are widely separated?
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