Waves
What is a wave?
• A disturbance that travels in a medium (or
vacuum for electromagnetic waves)
transferring energy and momentum from
one place to another.
Types of Waves
• Mechanical waves
– Require a material medium to travel through
– Sound, water
• Electromagnetic waves
– Can travel through a vacuum
– Light
Transverse Waves
• The particles move perpendicular to the
wave motion.
http://www.schulphysik.de/suren/Applets/Waves/Twave01/Twave01Applet.html
Longitudinal Waves
• The particles move parallel to the wave
motion.
http://www.schulphysik.de/suren/Applets/Waves/Lwave01/Lwave01Applet.html
Describing Waves
• Wavelength (λ)
– Shortest distance between two points that are
in phase on a wave
• Frequency (f)
– Number of vibrations per second
– Number of crests passing a fixed point per
second
• Period (T)
– Time for one complete wavelength to pass a
given point
– Time for a particle to undergo one complete
oscillation
• Amplitude (A)
– Maximum displacement of a wave from its
rest (equilibrium) position
Wave Equation
• When a source of a wave undergoes one
complete oscillation the wave it produces
moves forward one wavelength (λ)
• Since there are f oscillations per second,
the wave progresses fλ during this time
• Therefore the velocity of a wave (c) is
given by
c  f
Sound Waves
• Sound waves are produced by vibrations
• The vibrating source moves the nearby air
particles sending a disturbance through
the surrounding medium as a longitudinal
wave
• Sound is a mechanical wave and thus
requires a medium
Speed of Sound
• The speed of sound depends on two
things:
– The medium it is traveling in
• Sound travels faster in in a more dense medium
– The temperature of the medium
• Sound travels slower as the temperature
decreases
Speed of Sound in Various Media
Electromagnetic Waves
• Produced when electrons undergo an
energy change
– Radio waves are produced by accelerating
electrons through an antenna
– Gamma rays are produced by particle decays
or other annihilation events
• Velocity = 3.0x108 ms-1
• Consist of a time-varying electric field and
its associated time-varying magnetic field
em wave propagation
• Since the human eye is sensitive to the
electric field component, the amplitude of
an electromagnetic wave is usually taken
as the wave’s maximum electric field
strength
Electromagnetic Spectrum
•
•
•
•
•
•
•
Radio (λ~1mm-100km)
Microwave (λ~1mm-30cm)
Infrared (λ~1µm-1000µm)
Visible (λ~440nm-700nm
Ultraviolet (λ~100nm-400nm)
X-ray (λ~30pm-3nm)
Gamma (λ<1pm)
Wave Characteristics
• Wavefront
– A surface that travels with a wave and is
perpendicular to the direction in which it
travels
• Ray
– A line showing the direction in which a wave
transfers energy and is perpendicular to the
wave front
Intensity of a Wave
• The loudness of a sound wave or the
brightness of a light depends on the
amount of energy that is received by an
observer
• The intensity (energy) is proportional to
the square of the amplitude: I  A2
• Loudness and brightness are intensities
perceived by the observer and are related
to frequency
• The intensity of the wave decreases as the
distance between the source and the
observer increases
• The wave spreads out over an area
resulting in the relationship I  x 2
Principle of Superposition
• When two (or more) waves meet the total
displacement is the vector sum of the
individual displacements
• Having interacted, the waves continue on
their way as if they had never met at all
Interference
• When waves add together to give a total
displacement LESS than the original
waves it is called destructive
interference
• When waves add together to give a total
displacement GREATER than the original
waves it is called constructive
interference
Polarization
• Transverse waves have a unique property
call polarization
• Polarization of a transverse wave restricts
the direction of the oscillations to a plane
perpendicular to the direction of
propagation
http://micro.magnet.fsu.edu/primer/java/polarizedlight/filters/
Polarization of Light
• Étienne-Louis Malus (1809) showed that
when unpolarized light reflected off a glass
plate it could be polarized
• Sir David Brewster (1812) showed that
when unpolarised light was incident on an
optically dense surface (like glass) at a
specific angle (called Brewster’s angle),
the light is completely polarized
www.ryerson.ca/~kantorek/ELE884/Polarization.htm
• Edwin Land (1928) developed a material
with a molecular structure that only allows
a specific orientation of the electric field to
go through (called a Polaroid J sheet)
Malus’s Law
• Consider a polarized light whose electric
field Eo makes an angle θ with the
transmission axis of a second polarizer
(analyser)
• We can split the electric field into its
horizontal and vertical components
• In this case only the vertical component can
pass through giving
E  Eo cos 
• Transmitted intensity is proportional to the
square of the electric field so…
I  I o cos 2 
Io
- Incident intensity
Practical Uses of Polarizers
•
•
•
•
Polarized sunglasses
LCD panels
Stress analysis of some plastics
Some chiral (asymmetric) molecules are
optically active
Reflection
•
http://www.schulphysik.de/suren/Applets/Waves/TwaveRefTran/TwaveRefTranApplet.html
• 1 Dimensional wave fixed end
Reflected wave is
inverted
• 1 Dimensional wave free end
Reflected wave is
not inverted
• 2 Dimensional reflection
– The angle of incidence (measured from a line
normal to the surface) is equal to the angle of
reflection (measured from a line normal to the
surface)
Refraction
• When a wave
travels from one
medium to another
– Frequency of the
wave remains
constant
– Velocity of the
wave changes
– Some of the wave
is reflected
Snell’s Law
• Relates the incident wave to the refracted
wave
n1 sin2 v2


n2 sin1 v1
• n is the index of refraction
Diffraction
• Italian priest Francesco Grimaldi published
the first detailed observation and
description of diffraction in 1665 (two
years after his death)
• When waves pass through a narrow gap
or slit, or when their path is partially
blocked by an object, the waves spread
out into what one would expect to be a
shadow region
www.practicalpedal.com/photographcfo/Diffraction-in-Physics.html
physics2life.blogspot.ca/2008_10_01_archive.html
www.gearthblog.com/blog/archives/2012/01/wave_mechanics_in_google_earth.html
Tom leigh1
www.flickr.com/photos/tomleigh/3287584946/
maykan.wordpress.com/tag/science-fiction/
• A distinctive pattern appears a distance
away from the slit (or barrier) when the
wave hits a wall
cronodon.com/Atomic/Photon.html
• There is a bright spot in the middle with
alternating dark and bright spots on either
side
www.a-levelphysicstutor.com/wav-light-diffr.php
laser.physics.sunysb.edu/~mkorn/lecture/
interventions-mesures-physiques-evreux.e-monsite.com/pages/optique/diffraction-par-une-fente.html
• This happens because the paths of the
wave from each end of the slit (or side of
the barrier) are different lengths than the
path from the middle resulting in areas of
constructive and destructive interference
hyperphysics.phy-astr.gsu.edu/%E2%80%8Chbase/phyopt/sinvar.html
Path Difference
• When the path length of two coherent
waves differs by one-half wavelength, the
result will be total destructive interference
www.physicsclassroom.com/Class/light/u12l3b.cfm
• When the path length of two coherent
waves differs by one wavelength, the
result will be total constructive interference
www.physicsclassroom.com/Class/light/u12l3b.cfm
Double Slit Interference
• If a wave passes through two slits, then
the wave will diffract through both slits
resulting in two coherent (in phase) waves
• These two waves will overlap creating
areas of constructive and destructive
interference
www.mghs.sa.edu.au/Internet/Curriculum/Science/Stage2/Physics/stage2Physics.htm
• For light, we can observe this pattern on a
screen
sciencesummit.wordpress.com/2011/05/12/davisson%E2%80%93germer-experiment/
• Thomas Young performed this experiment
in 1801
– Therefore, double slit diffraction with light is
often referred to as Young’s experiment
• When light is used, the light is passed
through a single slit first such that it is
coherent (a laser could also be used)
img.wikinut.com/img/8zlnmjhvlc1fv1f./jpeg/0/The-Double-Slit-Experiment.jpeg
GIPHOTOSTOCK/SCIENCE PHOTO LIBRARY
www.sciencephoto.com/media/157198/enlarge
tsgphysics.mit.edu/pics/P%20Interference/Q2-P10-Laser-Diffraction-and-Interference-still.jpg
• Notice that two patterns exist
– A series of equally spaced bright and dark
spots and a pattern like the single slit
• This happens because there is still a
diffraction pattern from each slit and this
pattern is superimposed on the
interference pattern from the two waves
• If we add more slits the bright fringes get
narrower
www.unistudyguides.com/wiki/Interference_and_Diffraction
Diffraction Grating
• A diffraction grating is a natural
consequence of the effect on the
interference pattern when the number of
slits is increased
• Diffraction gratings are used to produce
optical spectra
• Typically contain 600 slits (or lines) per
mm with very small spacing between the
slits
www.rapidonline.com/Education/Diffraction-Grating-Slide-600-lines-per-mm-52-9005
www.looseinthelabscience.com/index.php/cat-supplies/cat-light/defraction-grating-glasses.html
reflectingreflecting.blogspot.ca/2009_11_01_archive.html
webinarsunleashed.com/v/account/themes/2.0/assets/ckeditor/plugins/pagebreak/images/diffraction-grating-film
www.askamathematician.com/wp-content/uploads/2011/05/Diffraction-grating.jpg
reednightingale.com/projects/physical/laserSpirograph/DSCN0025.JPG
Thin Films
• When light is incident on a thin film (oil,
soap) part of the light reflects off the
surface and some of the light is refracted
into the film
• When the refracted light hits the bottom of
the film it is once again both reflected and
refracted
• This process can occur several times for
the same incident wave
www.ualberta.ca/~pogosyan/teaching/PHYS_130/FALL_2010/lectures/lect34/lecture34.html
• When the light reflects off the top of the
film it undergoes a phase shift of 180° (or π
radians)
• Depending on the thickness of the film this
will result in either constructive or
destructive interference at the surface
John (ex-user Guinnog)
en.wikipedia.org/wiki/Thin-film_interference#mediaviewer/File:Dieselrainbow.jpg
www.tuks.nl/Mirror/labman.phys.utk.edu/Thin%20films.htm
www.tufts.edu/as/tampl/projects/micro_rs/theory.html
www.flickr.com/photos/gianpiero1966/14835899563/