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

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

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

5. Periodic Wave Source is a continuous vibration Source is a continuous vibration The vibration moves outward The vibration moves outward

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

7. Frequency and Period Frequency, f, is number of crests that pass a given point per second Frequency, f, is number of crests that pass a given point per second Period, T, is time for one full wave cycle to pass Period, T, is time for one full wave cycle to pass T = 1/f f = 1/T T = 1/f f = 1/T

8. Wave Velocity Wave velocity,v, is the velocity at which any part of the wave moves (propagates) Wave velocity,v, is the velocity at which any part of the wave moves (propagates) If wavelength =  v = f If wavelength =  v = f 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? 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? = Lambda = Lambda

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

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

11. Longitudinal Wave Can be thought of as alternating compressions and expansions or rarefactions Can be thought of as alternating compressions and expansions or rarefactions

12. Longitudinal Wave

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

14. Waves and Energy Waves with large amplitude carry more energy than waves with small amplitude Waves with large amplitude carry more energy than waves with small amplitude Goes as square of A Goes as square of A

15. Resonance Occurs when driving frequency is close to natural frequency (all objects have natural frequencies at which they vibrate) 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

18. Resonance Driving an object at its own natural frequency Driving an object at its own natural frequency

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

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

21. Reflection Law of reflection: Law of reflection: Angle of Incidence equals angle of Reflection Angle of Incidence equals angle of Reflection

22. Hard Reflection of a Pulse Reflected pulse is inverted Reflected pulse is inverted

23. Soft Reflection of a Pulse Reflected pulse not inverted Reflected pulse not inverted

24. Soft (free-end) Reflection

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

26. Formation of Standing Waves Two waves moving in opposite directions Two waves moving in opposite directions

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

28. Standing Wave Patterns on a String “Fundamental” = “Fundamental” =

29. First Harmonic or Fundamental

30. Second Harmonic

31. Third Harmonic

32. Wavelength vs. String length

33. String length = How many waves? L =

34. String length = How many waves? L = 3/2 

35. Wavelength vs. String Length Wavelengths of first 4 harmonics Wavelengths of first 4 harmonics L f =v

36. Frequencies are related by whole numbers Example Example f 1 = 100 Hz fundamental f 1 = 100 Hz fundamental f 2 = 200 Hz 2 nd harmonic f 2 = 200 Hz 2 nd harmonic f 3 = 300 Hz 3 rd harmonic f 3 = 300 Hz 3 rd harmonic f 4 = 400 Hz 4 th harmonic f 4 = 400 Hz 4 th harmonic etc etc Other frequencies exist but their amplitudes diminish quickly by destructive interference Other frequencies exist but their amplitudes diminish quickly by destructive interference

37. Wave velocity on a string Related only to properties of medium Related only to properties of medium Does not depend on frequency of wave Does not depend on frequency of wave v 2 = T/m/l Tension divided by mass per unit length of string v 2 = T/m/l Tension divided by mass per unit length of string

38. Standing Waves in Open Tubes

39. First Three Harmonics in Open Tube Amplitudes are largest at the open ends Amplitudes zero at the nodes f 1 = v/2L f 2 = v/L f 3 = 3v/2L Just like the string!

40. Tube Closed at One End L  /4 L =  /4 L =  /4 No even harmonics present f = v air /

41. Tube Closed at One End L  /4 L =  /4 L =  /4 No even harmonics present f = v air / f 1 = v/4L f 3 = 3v/4L f 5 = 5v/4L

42. Example For a closed one end organ pipe to make a 20 Hz fundamental, what length must it have? Use v = 340 m/s. For a closed one end organ pipe to make a 20 Hz fundamental, what length must it have? Use v = 340 m/s. L = v/4f = 4.25 m L = v/4f = 4.25 m What other frequencies will be heard? What other frequencies will be heard? Odd multiples only; 60 Hz, 100 Hz, 140 Hz etc Odd multiples only; 60 Hz, 100 Hz, 140 Hz etc

43. Beats Two waves of similar frequency interfere 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 Diagrams and animations courtesy of Tom Henderson, Glenbrook South High School, Illinois