Physics 2214 Assignment 7
Concepts:
Energy and power in waves
Electromagnetic waves
Fourier analysis, nonsinusoidal 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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 Spring '12
 Davis
 Energy, Power, Light, Cornell University

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