Ph12a Solution Set 7
November 22, 2013
6.14 The dispersion relation for a system of coupled pendula is given by eq. 90
of section 2.4:
K
ka
g
+ 4 sin2
l
M
2
2 (k ) =
g
l
The lower cuto frequency is
c
Ph12a Solution Set 8
December 6, 2013
9.4 The geometry of this problem is illustrated in Fig. 1. The light entering
the two slits will be reasonably coherent when the path dierence to the
two slits fr
1
Physics 12a Fall Term, 2013
Cover Page
Final Examination
This exam covers Chapters 16 and Chapter 9.19.6 in Crawford, as well as the
topics discussed in class, in the handouts, and in the homework.
1
Physics 12a Fall Term, 2013
Cover Page
Midterm Examination
This exam covers Chapters 13 in Crawford, as well as the topics discussed in
class and in the handouts through 29 October, as well as the h
Ph12a Solution Set 6
November 19, 2013
5.5 a) The reection coecient is given in Eq. 37 on page 243:
RV =
Z2 Z1
.
Z2 + Z1
So RV = 1 . This gives the amplitude of the reected wave:
3
Aref = Ainc RV = 3.
Ph12a Solution Set 5
November 7, 2013
4.8 For a single cylindrical wire of radius r, making a Gaussian pillbox of
cylindrical shape with radius R, r < R < r + D, parallel to the axis of the
wire, and
Ph12a Solution Set 1
October 17, 2013
1.15 The equations of motion for two coupled oscillators can be put in the form
d2 a
= a11 a a12 b
(1)
dt2
d2 b
= a21 a a22 b
(2)
dt2
Suppose we have two solution
Ph12a Solution Set 2
October 18, 2013
2.12 In a given mode with wavenumber k , the displacement is given as
= cos(t + )(A sin kz + B cos kz ),
where = cs k and cs = T0 /0 . Since the ends of the stri
Ph12a Solution Set 3
October 25, 2013
2.35 The general motion of the string can be expressed as a linear combination
of normal modes, each with its own phase:
(x, t) =
An sin (n t + n ) sin kn x
n
wh
Solutions for 2013 Midterm Exam
Phys. 12a
H. J. Kimble
(Dated: November 6, 2013)
PROBLEM 1: SIMPLE OSCILLATORS
Write an equation of motion and give the frequency for free oscillation of each of the
sy