Physical chemistry III
PROBLEMS
SS 2007
Exercise II
These exercises refer to chapter 3 of the script, which recapitulates central concepts in
physics. Make sure that you know them well before you do your exercises…
1.
Wave equation
Consider a guitar string fixed at both ends, between x=0 and x=2. The displacement away
from the equilibrium position of the string portion located between x and x+dx at time t is
called
(x,t)
. At time t=0, the string is at its equilibrium position, but an initial speed is given
all along the string, so that :
(eq. 1)
( ,0)
2
x
x
t
y
¶
=

¶
a) The wave equation describing the motion of this string is :
(eq. 2)
2
2
2
2
0
( , )
( , )
x t
x t
x
T
t
r
¶
¶
=
¶
¶
.
Give a comprehensive summary of the laws and approximations necessary to obtain eq. 2. Is
this equation dependent on the initial or boundary conditions? Mention some other fields of
physics described by the same kind of wave equation.
b) Write down the two harmonic oscillatorlike differential equations (like eq. 1 p. 12 of the
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 Spring '09
 haiza
 Frequency, Fundamental physics concepts, Nuclear magnetic resonance

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