Interference in a one-dimensional medium
Consider a slinky stretched
between two points. If we abruptly displace the spring at right
angles to its length, a pulse is launched along the spring. If
several pulses are created in short order, each will hold its
place in line because waves travel at some characteristic speed
for the medium. For pulses traveling in the same direction, watching
this gets old early. But what if the pulses are headed toward
each other on a collision course. What happens when they meet?
if the two combining pulses have displacements in the same direction,
the displacements add constructively, momentarily producing a
larger pulse, before continuing on as though nothing had happened.
Think of this event as one wave climbing over the other. If the
combining pulses have displacements on different sides of the
slinky, the pulses combine to produce a smaller wave, perhaps
even no wave at all. Once again the waves emerge from this momentary
union as though nothing special had happened. Keep in mind that
even if the two pulses disapppear for a moment, they must reappear.
Each pulse carries energy;for them to combine destructively and
vanish would be a violation of the law of conservation of energy.
Visit the applets in the boxes below to get a feel for this
O-123 |
The simplest case: two pulses combining
on a one-dimensional medium. http://www.phy.ntnu.edu.tw/java/wave/impulse.html http://id.mind.net/~zona/mstm/physics/waves/interference/waveInterference1/WaveInterference1.html http://www.phy.ntnu.edu.tw/java/waveSuperposition/waveSuperposition.html |
Sine waves are easy to generate and relatively easy to add, although the sums can look pretty ugly pretty quickly. Try these on for size
O-124 |
Let's generate two transverse
wave trains and add them together http://www.physics.brocku.ca/faculty/sternin/teaching/mirrors/superwaves/supers.html http://coral.lili.uni-bielefeld.de/~frederek/java/Sinus/added.html http://www.uno.edu/~jsulliva/java/superposition.html http://coral.lili.uni-bielefeld.de/~frederek/java/Sinus/added.html |
Pretend that we send a series of pulses
down a slinky that is tethered at the far end. The wave will reflect
from the far end and return to the source with its displacement
changed from a crest to a t rough and from trough to a crest.
If the returning waves encounter new incoming waves that are identical,
a wave pattern is created in which the waves simply undulate,
that is, the left-to-right and right-to-left motion of the waves
appears to vanish. Understand that a wave is moving through this
space left to right and another right to left. The waveform only
has the appearance of standing still and is called, sit down for
this. a standing wave. This phenomenon has significant
importance in music where standing wave patterns are the essence
of resonance.
Resonance occurs when waves, previously created
and sent through a medium, combine constructively wth new waves
now being launched. Resonance is most easily explained using mechanical
waves. Consider a child swingng on a swing at some frequency.
Consider the parent as a pushing machine, extending his/her arms
with the same frequency as the child. If the parent is properly
placed, pushing forward just as the child arrives, the parent
push adds to the child's displacement. If the parent is not properly
placed, the parent push works against the swinging child's and
resonance is not achieved.
For a good explanation of light interference, go to
http://www.colorado.edu/physics/2000/index.pl
Interference in a two-dimensional medium
Consider two point sources ( S1 & S2) of waves producing transverse waves of some arbitrary wavelength on pan of water. For now the sources are in phase and produce identical waves at the same time. The waves emanate from each source as circular wave fronts traveling in all directions in this two-dimensional medium. We choose some arbitrary point P where we can observe how the contribution from each source will add together. |
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Visit Mr. Hwang's applet and see a diagram similar to the one at left. Place the cursor where two crests meet; this is where one line crosses another (crest meets crest). Look at the path length difference illustrated in the box. You will note it to be very close to a whole number of (or even number of half) wavelengths. Now place the cursor at a point a where a line crosses a trough (the space between lines); this is a point of destructive interference. You will note that the path length difference is an odd number of half wavelengths. |
These are called Moire patterns
http://www.msu.edu/user/brechtjo/physics/interference/interference.html
http://webphysics.davidson.edu/Applets/Ripple/Ripple.html
http://www.netzmedien.de/software/download/java/interferenz
http://surendranath.tripod.com/DblSlt/DblSltApp.html
http://www.phy.ntnu.edu.tw/java/doubleSlit/doubleSlit.html
http://www.microscopy.fsu.edu/primer/java/doubleslit/index.html
http://www.bpreid.com/samples.html
applet central
http://www.uncwil.edu/people/hermanr/phy101/Applets.htm
http://www.cbu.edu/~jvarrian/applets/waves1/lontra_g.htm
An applet view of the EM spectrum
http://www.colorado.edu/physics/2000/index.pl
Young's Two-Slit Experiment with Laser
Light
http://www.colorado.edu/physics/2000/applets/twoslitsa.html
Constructive
and Destructive Wave Interference
http://www.colorado.edu/physics/2000/applets/fourier.html
http://lectureonline.cl.msu.edu/~mmp/applist/Spectrum/s.htm
A double slit will separate white light into a continuous spectrum of visible color. What happens when a source gives off only a small portion of that spectrum?
Click on the element and see its bright
line spectrum
http://javalab.uoregon.edu/dcaley/elements/Elements.html
http://www.phys.virginia.edu/classes/252/spectra.html
Go to http://www.glenbrook.k12.il.us/gbssci/phys/Class/light/u12l1b.html to view a site that closely models my classroom talk about this.
wave propagation & waveform applets
http://www.journey.sunysb.edu/ProjectJava/WaveInt/home.html
Go to homework problems - double slits
This first applet shows very nicely what
happens to te light pattern when variables are changed
http://webphysics.ph.msstate.edu/jc/library/24-3b/simulation.html
http://www.holostudios.com/holohelper/interference.html
derivation of Young's experiment equations
http://www.phys.ualberta.ca/~trpk/phys100/physopt/lite_int.html
color sim
http://webphysics.ph.msstate.edu/jc/library/24-3b/simulation.html
http://www.phy.ntnu.edu.tw/java/propagation/propagation.html
This first applet shows very nicely what
happens to te light pattern when variables are changed
http://webphysics.ph.msstate.edu/jc/library/24-3b/simulation.html
http://www.ece.gatech.edu/research/ccss/education/Java/1998.Winter/Projects/pierce-woods/project/bin/projApp.htm
This page was last modified by mgosselin on 10/08/2005