1. Vibrations and Waves Waves 2011-2012

2. Periodic Motion Periodic motion – a motion that repeats in a regular cycle. Simple harmonic motion – results when the restoring force on an object is directly proportional to the object’s displacement from equilibrium

3. Periodic Motion Period – T – time needed for an object to repeat one complete cycle Amplitude – the maximum distance that the object moves from equilibrium

4. Mass on a Spring

6. Pendulums

7. Resonance Occurs when small forces are applied at regular intervals to a vibrating or oscillating object and the amplitude of the vibration increases. Special form of SHM in which the additions of small amounts of force at specific times in the motion of an object cause a larger and larger displacement.

8. Parts of a Sine Wave crests – the high points of a wave troughs – the low points of a wave amplitude – the distance between the equilibrium point and the top of a crest (or bottom of a trough) wavelength – the distance between identical points on a wave

9. Parts of a Sine Wave wavelength amplitude crest trough

10. Calculating Frequency and Period Frequency Period

11. Wave Speed The speed of a wave depends on the medium through which the wave moves. The speed, wavelength, and frequency are related.

12. Transverse Waves Whenever the motion of the medium is at right angles to the direction in which a wave travels

13. Longitudinal Waves The particles move along the direction of the wave rather than at right angles to it.

14. Interference Interference pattern – waves that are in the same plane can overlap and interfere with one another Constructive interference – when the crest of one wave overlaps the crest of another, their individual effects add together Destructive interference – when the crest of one wave overlaps the trough of another, their individual effects are reduced

15. + = + = Constructive Interference Destructive Interference

16. Standing Waves Standing wave – Suppose a rope is attached to a wall. You shake the rope up and down and cause a sine wave. This is a standing wave. Node – point on the rope where there is no change in amplitude Antinode – points on the rope where there is maximum amplitude

18. Reflected Waves When a wave encounters a boundary, it will reflect back. The way in which it reflects will vary depending on whether it encounters a fixed or free boundary.

19. Fixed Boundary A fixed boundary is when a wave encounters a fixed surface. This would occur for a rope attached to a wall.

20. Reflection at a Fixed Boundary Incident wave Reflected wave

21. Free Boundary A free boundary occurs when, for example, a rope is attached to a post and is free to move up and down at the end.

22. Reflection at a Free Boundary Incident wave Reflected wave

23. Less DenseMore Dense Incident Pulse Reflected PulseTransmitted Pulse

24. More DenseLess Dense Incident Pulse Reflected PulseTransmitted Pulse

25. Reflection and Refraction Reflection ◦ Waves bounce back off of a surface that they encounter. Refraction ◦ Waves bend and pass through a surface that they encounter.