Name:______________________________
PHYSICS 306 – Practice EXAM
Except for the first problem, answer all questions with all steps for full credit. For the first
problem, select your answers with VERY BRIEF explanations.
Problem 1 (30 points total)
Please answer the following SINGLE choice questions.
1) (3 pts) The wave equation discussed in this course can be written as
2
2 y
2  y

c
t 2
x 2
One solution for this equation is
A. f(x+ct2)
B. f(x+ct)
C. f(x+ct3)
2) (3 pts) Which statement below regarding the electromagnetic (EM) waves is
WRONG?
A. The electrical and magnetic energy densities in EM waves are equal
B. The electric field, the magnetic field, and the propagation direction are all
perpendicular for EM waves in free space.
C. The electrical and magnetic field amplitudes in EM waves are equal
3) (3 pts) Which definition for Quality factor Q is NOT accurate?
A. Q/2 gives the ratio between the total energy stored and energy lost per cycle
B. Q/2 gives the number of cycles during which energy decreases to 1/e of E0
C. Q has the same dimension as angular frequency
4) (3 pts) Below we show irradiance vs. time for two light pulses which are plotted
using the same scale for the time axis. Which one has broader spectrum width?
A. Left panel
B. Right panel
C. No enough information to judge
A. 10
B. 3 C. 300
Displacement Amplitude
5) (3 pts) Which of the following values are closest to the Q of the driven oscillator
whose response is shown above?
80
40
A
B
C
0
0
500
1000
1500
2000
Angular frequency ()
6) (5 pts) Which pattern below corresponds to far field diffraction from a double slit
screen illuminating by a point source behind it?
A.
B.
C.
7) (5 pts) Spatial fringes can be formed in the intersecting region of two light waves
cross with an angle Which one of the following two spatial images corresponds
to bigger between the two light waves?
A. Left panel
B. Right panel
C. No enough information to judge
8) (5 pts) Given a time-dependent wave group function f(t) as below. Which one is
F(ω), complex Fourier transform of f(t)?
A. sin(/2)/(/2)
B. cos()/
C. sin()
Problem 2 (20 points)
A sinusoidal wave of amplitude 3m travels with a frequency of 10 Hz on a string of linear
mass density =0.2 kg m-1, length 10m and tension 10N.
a) Write an expression for the wave transverse displacement
b) Calculate the wave speed and wave number
c) Write down the complete waveform.
We know light can be characterized as sinusoidal electromagnetic waves.
d) If we consider light passes normally through a glass plate (n=1.5) suffering only
one air to glass and one glass to air reflection. What is the loss of intensity?
Problem 3 (20 points total)
A transverse wave travelling along a string given by:

  z, t   0.5m  cos 50 s 1  t  4 m 1  z

where the units within the parentheses are meters and seconds
a) Verify that this expression is a solution for the wave equation
b) Determine the amplitude, wavelength and period of the wave.
c) Determine the wave phase velocity.
d) Find the transverse displacement and transverse velocity of the string at z=5m and
t=0.1sec.
e) Given that tension on the string is supplied by a pulley with a weight attached to a
pulley. The weight has a mass 10 times the mass of the string, calculate the
length of the string
Problem 4
We are now going to consider the propagation of transverse waves along a linear array of
atoms, mass m, in a crystal lattice where we define tension T to be the elastic force between
the atoms and a to be the separation between the atoms. The general dispersion relation
(that is the frequency  as a function of wave number k) for the transverse waves reads as:
1. Sketch the dispersion in the range of k [0,π/a]
2. Discuss the behaviors of the wave at long wavelengths or low values of the wave
number k
3. Derive the phase velocity and group velocity of the wave.