1. PHYS16 – Lecture 34 Waves December 3, 2010 “Interference is much clearer in HD”

2. Outline for Oscillations Simple Harmonic Motion – Position, Velocity, Acceleration – Force – Energy – Phase – Damping – Resonance Waves – Mechanical waves – Interference – Standing waves

3. Mechanical Waves

4. A propagating oscillation that moves through a medium Transverse – water waves Longitudinal – sound waves

5. 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

6. Wave Properties Period – T high period medium period low period

7. Wave Properties Period – Wavelength and Wave number – http://seagrant.uaf.edu/marine-ed/curriculum/images/stories/grade7/wave.jpg

8. Wave Properties Period – Wavelength and Wave number – http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/Images_specific/wave_def.gif

9. Wave Properties Period – Wavelength and Wave number – Wave speed – http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/Images_specific/wave_def.gif

10. Mechanical Wave – Position of Particle Plane Wave Higher Dimension Wave

11. Ripple Tank Simulation

12. Example Question 1 PhET website

13. Example Question 2 PhET website

14. Example Question 2 PhET website Speed = Period = Wave number = Wavelength = 330 m/s 0.0038 s 5.0m -1 1.25 m

15. Example Question 3 Sand is placed on the vibrating plate below. Which apparatus is vibrating the plate with the highest wave number?

16. Wave on a String

17. 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 PhET website

18. 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

19. Wave on String Simulation PhET website

20. Example Question PhET website

21. Superposition, Interference, and Standing Waves

22. 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

23. Interference Destructive Constructive PhET website

24. Interference http://www.rp-photonics.com/img/interference2_s.png

25. 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 Node Antinode

26. Example Question 1 PhET website

29. 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 m B)2 m C)1 m D)0.5 m E)0.25 m

30. 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