M Sittig
AP Physics B
Summer Course 2012
2012 年 AP 物理 B 暑假班

Waves


Waves are all around us.
They are a form of simple harmonic motion.

Transverse and Longitudinal

Transverse and Longitudinal

Wave Terminology

Wave Speed

Velocity of a wave
Wave speed
(m/s) v
  f
Wavelength
(m)
Frequency
(1/s)

Practice Problem

A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along a rope in 10.0 s . What is the wavelength?

Practice Problem

The displacement-time graph and displacementdistance graph of a particular wave are shown below. What is the speed of the wave?

Interference


When two waves overlap, interference occurs.
Superposition principle:
When two or more waves occupy the same space at the same time, the displacements
(+ and -) add at every point on the waves.
The resultant displacement at any point is the sum of the separate displacements of the waves.

Constructive Interference

It occurs whenever two waves combine to make one wave with a larger amplitude.

Constructive Interference

Destructive Interference

When the amplitudes of two waves combine producing a smaller amplitude. (The two waves need not cancel each other totally.)

Destructive Interference

Interference
 http://physics.ham.muohio.edu/waveapplet s/pulseadd.htm

Interference
A B
DESTRUCTIVE
CONSTRUCTIVE

Interference
A B
DESTRUCTIVE
CONSTRUCTIVE

Standing Waves


A standing wave is a wave that appears to be stationary, even though it is really two separate waves interfering as they pass through each other.
It is due to superposition of incident and reflected waves of same frequency, amplitude and wavelength traveling in opposite directions.

Standing Waves

Standing Waves
 http://www.phys.unsw.edu.au/jw/module1
_nodes.swf

Standing Waves

Standing Waves

Standing Waves


There are points where the displacement is always zero. These points are called nodes of the standing wave.
Points which have the greatest amplitude are called the antinodes.

Standing Waves

Standing Waves

Standing Waves

Standing Waves

Number of loops in standing wave depends on the vibration frequency.
f
2f
3f
4f

f
Standing Waves in Pipes

Number of loops in standing wave depends on the vibration frequency.
 v /
 
This FIRST SOUND is called the
FUNDAMENTAL
FREQUENCY or the
FIRST HARMONIC.

Standing Waves in Pipes

Harmonics are
MULTIPLES of the fundamental frequency

In a closed pipe, you have a NODE at the
2nd harmonic position, therefore
NO SOUND is produced

Standing Waves in Pipes

You will get your
FIRST sound when the length of the pipe equals one-half of a wavelength.

Example Problem

The speed of sound waves in air is found to be 340 m/s. Determine the fundamental frequency (1st harmonic) of an open-end air column which has a length of 67.5 cm.

Practice Problem

The windpipe of a typical whooping crane is about 1.525-m long. What is the lowest resonant frequency of this pipe assuming it is a pipe closed at one end? Assume a speed of sound of 340 m/s.

Doppler Effect

Imagine a motorcycle or racecar, how the frequency changes (not volume).

Electromagnetic Waves

See EM Waves PPT .

Double Slit

See PPT: AP_Physics_B_-_Diffraction.ppt

Double Slit

Single Slit

Single Vs Double

Double in Real Life

Diffraction Gratings
 http://hyperphysics.phyastr.gsu.edu/hbase/phyopt/mulslidi.html

Review

See PPT: PPA6_ConcepTests_Ch_24.ppt

Example Problem

A viewing screen is separated from a double slit source by 1.2 m. The distance between the two slits is 0.030 mm. The second -order bright fringe (m=2) is 4.5 cm from the central maximum. Determine the wavelength of light.

Index of Refraction
 n, a number that describes how much light slows down (and bends) when it passes through a material.

Thin Films

Thin films




1. Count the phase changes.
2. The extra distance traveled in the material is a round trip (2t).
3. The wavelength in the material is λ n
=λ/n.
4. Apply 2t = mλ n
. If phase changes is even
(0, 2…) then integers for m means constructive interference, half-integers means destructive. If phase changes is odd
(1, 3…) then it is the reverse.

Example/Practice Problem





A thin film of material is to be tested on the glass sheet for use in making reflective coatings. The film has an index of refraction n f
= 1.38.
White light is incident normal to the surface of the film as shown below.
It is observed that at a point where the light is incident on the film, light reflected from the surface appears green (  = 525 nm). a. What is the frequency of the green light in air?
b. What is the frequency of the green light in the film? c. What is the wavelength of the green light in the film? d. Calculate the minimum thickness of film that would produce this green reflection.