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Homework # 4 (due Thursday, 10 February)
1. Consider a longitudinal wave
( 29
cos
ϖ
=

n
u
A
qna
t
in a monoatomic linear lattice of
atoms of mass
M
, spacing
a
and nearestneighbor interaction
C
.
(a)
Show that the total energy of the wave is given by
( 29
2
2
1
1
1
2
2
+
±
=
+

²
³
´
µ
¶
¶
n
n
n
n
n
du
E
M
C
u
u
dt
,
where
n
runs over all atoms.
(b)
Show that the timeaveraged kinetic energy is equal to the timeaveraged potential
energy.
(c)
Show that the total timeaveraged energy per atom is equal to ½
MA
2
2
.
2. Consider a linear chain in which alternative ions have masses
M
1
and
M
2
and only
nearest neighbors interact.
(a)
Discuss the form of the dispersion relation and the nature of the vibrational
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This note was uploaded on 09/21/2011 for the course PHYSICS 101 taught by Professor Wormer during the Spring '08 term at Aarhus Universitet.
 Spring '08
 WORMER
 Energy, Mass, Work

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