April 21, 2006
Physics for Scientists&Engineers 1
1
Physics for Scientists &
Physics for Scientists &
Engineers 1
Engineers 1
Spring Semester 2006
Lecture 51
April 21, 2006
Physics for Scientists&Engineers 1
2
Few points
!
SOCT (Student Opinion of Courses and Teaching) Online
Forms:
PHY 183
4/17/2006 – 5/12/2006
http://rateyourclass.msu.edu
!
Final Exam date:
Thurs. May 4, 810 pm
E100 VMC (Veterinary Medical Center) Bldg.
!
Clicker points (thru April 18) posted on LonCapa
•
Maximum points so far: 146
•
Scores out of
!
maximum = 73
April 21, 2006
Physics for Scientists&Engineers 1
3
Mathematical Description of Waves
!
Suppose member of chain at
x=0
oscillates with
!
Time delay for the oscillation to move distance
x
is
!
Then we can write for the wave
y (x,t)
:
0
(
0, )
sin(
)
y x
t
A
t
!
"
=
=
+
!
t
=
x
v
0
( , )
(0,
)
sin
x
x
y x t
y
t
A
t
v
v
!
"
#
$
#
$
=
%
=
%
+
&
’
&
’
(
)
(
)
( , )
(0,
)
x
y x t
y
t
v
!
"
April 21, 2006
Physics for Scientists&Engineers 1
4
Wave Number and wave function
Wave Number and wave function
!
Defining the wave number:
similar to
!
Note that
!
The wave function reads as:
!
One can check that:
y
(
x
,
t
)
=
A
sin
!
t
"
#
x
+
$
0
(
)
!
=
2
"
#
( ,
)
( , )
(
, )
( , )
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 Spring '08
 Wolf
 Physics, Coupled Oscillators, yn + yn

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