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