1. WAVES Vibrations that carry energy from one place to another

2. Types of Wave • Mechanical. Examples: slinky, rope, water, sound, & earthquake • Electromagnetic. Examples: light, radar, microwaves, radio, & x-rays

3. What Moves in a Wave? • Energy can be transported over long distances • The medium in which the wave exists has only limited movement • Example: Ocean swells from distant storms Path of each bit of water is ellipse

4. Periodic Wave • Source is a continuous vibration • The vibration moves outward

5. Wave Basics - Vocabulary • Wavelength is distance from crest to crest or trough to trough • Amplitude is maximum height of a crest or depth of a trough relative to equilibrium level

6. Frequency and Period • Frequency, f, is number of crests (waves) that pass a given point per second • Period, T, is time for one full wave cycle to pass • T = 1/f f = 1/T (inverses or reciprocals) • Waves /second = seconds/wave = f T

7. Unit of Frequency • Hertz (Hz) • Second-1 same as 1/second or per second • Used to be “cycles per second”

8. Wave Velocity • Wave velocity,v, is the velocity at which any part of the wave moves • If wavelength = l, v = lf • Example: a wave has a wavelength of 10m and a frequency of 3Hz (three crests pass per second.) What is the velocity of the wave? Hint: Think of each full wave as a boxcar. What is the speed of the train?

9. v = lf l =v/f f = v/ l • l lambda = wavelength • f frequency • v is sometimes called velocity ofpropagation (speed wave moves in medium)

10. Example • A ocean wave travels from Hawaii at 10 meters/sec. Its frequency is 0.2 Hz. What is the wavelength? l = v/f = 10/0.2 = 50 m

11. Second example • What is the wavelength of 100 MHz FM radio waves? Use v = c = 3 x 108 m/s • l = v/f = 3 x 108 m/s ÷ 100 x 106 s-1 • = (300 x 106)÷ (100 x 106)m • = 3.0 m

12. Another example • Waves travel 75 m/s on a certain stretched rope. The distance between adjacent crests is 5.0 m. Find the frequency and the period. • f = v/l • f = 75 m/s ÷ 5.0 m = 15 Hz = 15 s-1 • T =1/15 = 0.066666 s

13. Longitudinal vs. Transverse Waves • Transverse: particles of the medium move perpendicular to the motion of the wave • Longitudinal: vibrations in same direction as wave

14. Longitudinal Wave • Can be thought of as alternating compressions (squeezing) and expansions or rarefactions (unsqueezing)

15. Longitudinal Wave

16. Sound Wave in Air • Compressions and rarefactions of air produced by a vibrating object

17. Waves and Energy • Waves with large amplitude carry more energy than waves with small amplitude

18. Resonance • Occurs when driving frequency is close to natural frequency (all objects have natural frequencies at which they vibrate) Tacoma Narrows bridge on the way to destruction– large amplitude oscillations in a windstorm

21. Interference • Amplitudes of waves in the same place at the same time add algebraically (principle of superposition) • Constructive interference:

22. Destructive Interference • Equal amplitudes(complete): • Unequal Amplitudes(partial):

23. Reflection • Law of reflection: Angle of Incidence equals angle of Reflection

24. Hard Reflection of a Pulse • Reflected pulse is inverted

25. Soft Reflection of a Pulse • Reflected pulse not inverted

26. Soft (free-end) Reflection

27. Standing Waves • Result from interference and reflection for the “right” frequency • Points of zero displacement - “nodes” (B) • Maximum displacement – antinodes (A)

28. Formation of Standing Waves • Two waves moving in opposite directions

29. Examples of Standing Waves • Transverse waves on a slinky • Strings of musical instrument • Organ pipes and wind instruments • Water waves due to tidal action

30. Standing Wave Patterns on a String • “Fundamental” =

31. First Harmonic or Fundamental

32. Second Harmonic

33. Third Harmonic

34. Wavelength vs. Stringlength

35. String length = How many waves? L = l

36. String length = How many waves? L = 3/2 l

37. Wavelength vs. String Length fl =v • Wavelengths of first 4 harmonics L

38. Frequencies are related by whole numbers • Example • f1 = 100 Hz fundamental • f2 = 200 Hz 2nd harmonic • f3 = 300 Hz 3rd harmonic • f4 = 400 Hz 4th harmonic • etc • Other frequencies exist but their amplitudes diminish quickly by destructive interference

39. Wave velocity on a string • Related only to properties of medium • Does not depend on frequency of wave • v2 = T/m/l Tension divided by mass per unit length of string

40. Standing Waves in Open Tubes

41. First Three Harmonics in Open Tube Amplitudes are largest at the open ends Amplitudes zero at the nodes

42. Tube Closed at One End L = l/4 L = 3l/4 L = 5l/4 No even harmonics present f = vair/l

43. Beats • Two waves of similar frequency interfere Beat frequency equals the difference of the two interfering frequencies

44. Acknowledgements • Diagrams and animations courtesy of Tom Henderson, Glenbrook South High School, Illinois