PHYSICS 002C
Lecture 06
April 09, 2010
Serway and Jewett Chapter 14.1-4
–
Interference
Clicker Q1:
The principle of superposition holds for a wave equation
which is
a)
pliniar;
b)
finial;
c) linear;
d)
similar
e)
linial.
Clicker Q2:
Interference occurs when two waves in a medium
a)
haplap;
b)
underlap;
c)
overlap;
d)
dewlap;
e)
lapstreak.
Clicker Q3:
A single frequency standing wave exhibits harmonic motion
a)
whenever it is a combination of two wavelengths;
b) nowhere;
c)
everywhere except at the nodes;
d)
only at the antinodes;
e)
only at
the nodes.
One type of interference
Chap 14.1
–
The Superposition Principle
The sum of two solutions to a
linear
wave equation is also a solution.
The definition of a
linear operator
b
(
x
,
y
,…)
that acts on a set of
functions
f
(
x
,
y
,…),
g
(
x
,
y
,…), … is that
b
(
x
,
y
,…)
[
af
(
x
,
y
,…)+
bg
(
x
,
y
,…)]=
Searchlight beams
passing
through
each other
a
b
(
x
,
y
,…)
f
(
x
,
y
,…)+
b
b
(
x
,
y
,…)
g
(
x
,
y
,…)
for all functions in the set and for all multipliers
a
,
b
, ….
A
linear wave equation
is of the form
b
(
x
,
y
,…,
t
)
f
(
x
,
y
,…,
t
)=0, so a sum
of two solutions
f
(
x
,
y
,…)+
g
(
x
,
y
,…) is also a solution.
Examples
:
Electromagnetic waves (light, radio, x-rays) in vacuum. Two light
beams scatter from each other (especially if their frequency is near
m
e
c
2
/
h
= 1.23559
10
20
Hz).
Superposition works if the amplitude is small even for a nonlinear
wave equation.
Gravity waves are inherently nonlinear because a gravitational field is
a source for more gravitational field:
field
(
x
,
y
,
z
,
t
)=
g
(
x
,
y
,
z
,
t
)
2
/8
c
2
.
Light waves in optical fibers are nonlinear at high amplitudes.