PHYS16 – Lecture 34
“Interference is much clearer in HD”
Waves
December 3, 2010
Outline for Oscillations
• Simple Harmonic Motion
–
–
–
–
–
–
Position, Velocity, Acceleration
Force
Energy
Phase
Damping
Resonance
• Waves
– Mechanical waves
– Interference
– Standing waves
Mechanical Waves
Mechanical Waves
• A propagating oscillation that moves through
a medium
Transverse – water waves
Longitudinal – sound waves
Mechanical Waves
• Waves use at least 1-3 space dimensions and
time…
– Ex. – Water waves propagate in x, move “up and down” in
y, and change position with time
– Ex. – Sound waves propagate in x, move “up and down” in
x, and change position with time
Wave Properties
• Period –
2
1
T


f
T
high
period
medium
period
low
period
Wave Properties
• Period –
2
1
T


f
• Wavelength and Wave number –   2

http://seagrant.uaf.edu/marine-ed/curriculum/images/stories/grade7/wave.jpg
Wave Properties
2
1
T


f
• Period –
• Wavelength and Wave number –   2

http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/Images_specific/wave_def.gif
Wave Properties
• Period –
2
1
T


f
• Wavelength and Wave number –  
• Wave speed –

v  f 

http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/Images_specific/wave_def.gif
2

Mechanical Wave – Position of Particle
Plane Wave
t  x v ,    v  2f v  2 
y ( x, t )  A sin( t  x  0 )
Higher Dimension Wave



y( x, t )  A( x ) sin( t  x  0 )
Ripple Tank Simulation
Example Question 1
PhET website
Example Question 2
PhET website
Example Question 2
Speed =
Period =
Wave number =
Wavelength =
330 m/s
0.0038 s
5.0m-1
1.25 m
PhET website
Example Question 3
• Sand is placed on the vibrating plate below.
Which apparatus is vibrating the plate with
the highest wave number?
Wave on a String
Wave on a String
• You can generate a wave on a string by pulsing
sting with your hand
• Speed of pulse/wave is related to tension in
string and mass density of string v  T 
PhET website
Propagation of Pulse
• If you advance the movie one frame point A will move…
(higher, lower, right, left)?
• If generate new pulse but more quickly than first then it will
be… (same, wider, narrower)?
• If generate new pulse but move hand higher than first then it
will be… (same, taller, shorter)?
• If generate new pulse with rope tightened then pulse will be…
(same, faster, slower)?
PhET website
Wave on String Simulation
PhET website
Example Question
PhET website
Superposition, Interference, and
Standing Waves
Superposition and Interference
• Superposition - When two stimuli overlap they
will superimpose, or the new stimulus will be
the sum of the two individual stimuli
• Interference – the superposition of two or
more waves, amplitudes sum together
– “out of phase” or phases shifted by 180 degrees
then they will “destructively” interfere
– “in phase” or phases not shifted then they will
“constructively” interfere
Interference
Constructive
Destructive
PhET website
Interference
http://www.rp-photonics.com/img/interference2_s.png
Standing Waves
• Standing waves – waves that constructively
interfere in cavity and “stand” in one spot
Node
http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter7_files/image023.gif
Antinode
Example Question 1
PhET website
PhET website
PhET website
Example Question 2
• A string of 0.25 kg/m is stretched to a tension
of 4 N between 2 plates that are 0.5 m apart.
What is the wavelength of the first harmonic
in the string?
A)
B)
C)
D)
E)
4m
2m
1m
0.5 m
0.25 m
Main Points - Waves
• Mechanical Wave – a propagating oscillation that
moves through a medium
v T 
• Superposition – wave amplitudes add together
• Interference – when two or more waves
superimpose (destructive -> less A and
constructive -> bigger A)
• Standing waves – waves that constructively
interfere within a cavity and appear to “stand” in
one spot