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Review
Vibrations and Waves
Restoring Force
F  kx
Important: the restoring force F is not
constant, but varies with position!
Energy in the Simple Harmonic
Oscillator
The Period of Oscillations
T  2 m / k
1
f 
k /m
2
Important: The period of simple
oscillations doesn’t depend on the
amplitude!!
The Simple Pendulum
T  2 L / g
The period doesn’t depend on the
mass of bob, it depends only on the
length of the thread.
Forced Vibrations; Resonance
The increase of amplitude near f=f0 is
known as resonance.
At what frequencies (if any) except
for f0 might be observed a
resonance?
1. You stand to the side of the low point of a child’s swing
and always push the child in the same direction. Which
of the following multiplies of the fundamental
frequency will not produce resonance: 1/3; ½; 1, or 2?
The wave velocity, v, is the velocity at
which wave crests (or any other point of
the waveform) move.
Important: Don’t confuse with the
velocity of a particle, oscillating in a
wave!
v

T
 f
Velocity of a Wave in a Stretched
String
FT
v
m/ L
Types of Waves
transversal
longitudinal
Interference
Interference refers to what happens
when two waves pass each other.
Principle of Superposition
In the region, where the waves overlap, the
resultant displacement is the algebraic sum of
their separate displacements. Crest is
considered positive and trough negative.
1. When you yell at your friend, are the air molecules that
strike his ear the same ones that were in your lungs?
Explain.
2. Which of the following properties affect the speed of waves
along a rope: amplitude of the pulse, shape of the pulse,
tension in the rope, and/or the mass per unit length of the
rope?
Sound and Music
Speed of Sound in the Air:
v=(331 + 0.6T) m/s,
Where T is the temperature in C.
The lowest three frequencies in the string
Interference and Sound Waves
Beats
Doppler Effect
1. How does the fundamental frequency of an organ pipe,
which is open at both ends, change as you close one of the
ends?
1. You have an organ pipe that resonates at frequencies of 300,
450, and 600 hertz but nothing is between. It may resonant at
lower and higher frequencies as well. Is the pipe open at both
ends or open at one end and closed at the other? How can you
tell?
2. Same for 500, 700 and 900 Hz.
3. An automobile sounding its horn is moving toward you at a
constant speed. How does the frequency you hear compare
with that heard by the driver?
Static Electricity
The Electroscope
An electroscope is a device that can be used for
detecting charge.
Coulomb’s Law
Q1Q2
F k 2
r
Units of Charge
1 Coulomb (C)
k  8.988 10 N  m / C  9.0 10 N  m / C
9
2
2
9
2
2
1. A handheld glass can be charged by rubbing it with silk or a
plastic bag while holding it in your hands. Would you
conclude from this that glass is a conductor or an insulator?
Why?
2. Why it is easier to charge a balloon on a dry day than on a
humid day?
1. When Coulomb was developing his law, he did not have an
instrument for measuring charge. And yet he was able to
obtain spheres with ½ ; 1/3; ¼;… of some original charge.
How might he have used a set of identical spheres to do
this?
The electric field E at a point in space is
defined as an electric force F, acting on a
positive test charge q divided by the
magnitude of the test charge

 F
E
q
1
Q
E
2
4 0 r
Field Lines
Electric Fields and Conductors
Important: electric field inside of good
conductor is zero!!!!
Important: any net charge on a good
conductor distributes itself on the
surface!!!!
Electric Potential and Potential
Difference
It’s useful to define the electric potential (or
simply the potential) as a potential energy per
unit charge:
PEa
Va 
q
Vba
E
d
Important: this simple formula for E
may be used only for uniform field!!!!