Review

Vibrations and Waves

Restoring Force

kxF Important: the restoring force F is not constant, but varies with position!

Energy in the Simple Harmonic Oscillator

The Period of Oscillations

mkf

kmT

/2

1

/2

Important: The period of simple oscillations doesn’t depend on the amplitude!!

The Simple Pendulum

gLT /2The 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!

fT

v

Velocity of a Wave in a Stretched String

Lm

Fv T

/

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

221

r

QQkF

Units of Charge

1 Coulomb (C)

229229 /100.9/10988.8 CmNCmNk

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

q

FE

204

1

r

QE

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:

q

PEV a

a

d

VE ba

Important: this simple formula for E may be used only for uniform field!!!!