phys16 – lecture 34
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PHYS16 – Lecture 34. Waves December 3, 2010. “Interference is much clearer in HD”. Outline for Oscillations. Simple Harmonic Motion Position, Velocity, Acceleration Force Energy Phase Damping Resonance Waves Mechanical waves Interference Standing waves. Mechanical Waves. - PowerPoint PPT PresentationTRANSCRIPT
PHYS16 – Lecture 34
Waves December 3, 2010
“Interference is much clearer in HD”
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 –
Thighperiod
mediumperiod
lowperiod
fT 12
Wave Properties
• Period –
• Wavelength and Wave number –
fT 12
2
http://seagrant.uaf.edu/marine-ed/curriculum/images/stories/grade7/wave.jpg
Wave Properties
• Period –• Wavelength and Wave number –
fT 12
2
http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/Images_specific/wave_def.gif
Wave Properties
• Period –
• Wavelength and Wave number –
• Wave speed –
fT 12
2
http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/Images_specific/wave_def.gif
fv
Mechanical Wave – Position of Particle
)sin(),(22 ,
0
xtAtxyvfvvxt
Plane Wave
Higher Dimension Wave
)sin()(),( 0 xtxAtxy
Ripple Tank Simulation
Example Question 1
PhET website
Example Question 2
PhET website
Example Question 2
PhET website
Speed =Period =Wave number = Wavelength =
330 m/s0.0038 s5.0m-1
1.25 m
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 Tv
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
Destructive
Constructive
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
http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter7_files/image023.gif
NodeAntinode
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) 4 mB) 2 mC) 1 mD) 0.5 mE) 0.25 m
Main Points - Waves
• Mechanical Wave – a propagating oscillation that moves through a medium
• 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
Tv