Chapter 19

1. Chapter 19 Vibrations and Waves

2. Vibration:A disturbance “wiggle” in time. • Wave:A disturbance in spaceand time.

3. Oscillatory Motion • The to-and-fro vibratory motion, such as that of a pendulum.

4. Simple Pendulum For small displacements, the period of the simple pendulum is related to its length (L) and the acceleration due to gravity (g) by the following:

5. Simple Harmonic Motion • is a type of oscillatory motion in which the motion repeats itself. • This motion is caused by a “restoring force” that acts in the opposite direction of the displacement.

6. Simple Pendulum • Under small displacements, the simple pendulum behaves as a harmonic oscillator. • For a pendulum, the “restoring force” is usually exerted byGRAVITY

7. Amplitude • The maximum displacement from some equilibrium (mid point) position. (Applies to both vibrations and waves.)

8. Mass-Spring System is Another Example of a Simple Harmonic Oscillator Live Demonstration

9. Wavelength • The distance between successive crests, troughs, or identical parts of a wave. • Common symbol used for wavelength is the Greek letter  - pronounced “lambda”

10. Sine Curve Wavelength  Crest Amplitude A Trough

11. Frequency:The number of vibrations per unit time. • Common symbols aref and the Greek letter - pronounced ”nu” • Period:The time in which a vibration is completed. • Common symbols are T and the Greek letter  - pronounced“Tau”

12. More on frequency • We can talk about the frequency of a vibration or of a wave. Frequency is measured in inverse seconds, or Hertz (Hz). • E.g.. • f = 10 cycles/sec = 10sec-1 = 10 Hz.

13. Frequency and Period are related • Frequency equals inverse Period. • Period equals inverse Frequency.

14. In symbols, this means... f = 1/T or  = 1/ and T = 1/f or  = 1/

15. Examples AM radio frequencies are measured in KiloHerts - (KHz). Kilo = one thousand = 1,000 = 1x103 . The period is 1/1,000Hz = 1x10-3 sec = 1millisecond (ms)

16. FM radio frequencies are measured in MegaHertz (MHz) • Mega = one million = 1,000,000 = 1x106 • The period is (1/1,000,000 Hz)= • 1x10-6 sec = 1 microsecond (s).

17. More Examples • Water waves might have a frequency of 2Hz (i.e. 2 cycles per second). • The corresponding period is equal to: • 1/f = 1/2Hz = 0.5 seconds

18. The AM and FM radio waves are examples of • Electromagnetic Waves • Light is another example of an • electromagnetic wave

19. The water waves are examples ofMechanical Waves Mechanical waves require a medium in which to propagate. Electromagnetic waves do not.

20. Wave Speed • The speed with which waves pass a particular point. • Common symbol used for wavespeed is the letter v.

21. In symbols, this is: v = /T • Wavespeed = wavelength / period but, since we already know that frequency is the same as inverse period ( f = 1/T), then we can also write this as v = f

22. A note as to why we use “v” • The letter v is used for velocity in general. • Velocity and speed are closely related. • Velocity is speed in a specific direction.

23. For Example • If I tell you I’m traveling at 55 miles/hour due north, I have told you my velocity • If I tell you I’m traveling at 55 miles/hour, I have told you my speed.

24. Types of Waves There are two types of waves 1) Transverse Waves. 2)Longitudinal Waves.

25. 1) Transverse Wave: A wave in which the vibration is in a direction perpendicular (transverse) to the direction in which the wave travels. e.g. Light waves. Waves on a string. Seismic “S”-waves.

26. 2) Longitudinal Wave: A wave in which the medium vibrates in a direction parallel (longitudinal) to the direction in which the wave travels. e.g.Sound. Seismic P-waves. http://www.physics.ohio-state.edu/133/demo/Lwave.gif

27. In a longitudinal wave, the medium has regions of compression and expansion which are along the direction of wave propagation. Regions ofexpansion are also called (rarefactions)

28. Interference A number of different waves can add, constructively or destructively. This is known as superposition. The superposition of two or more waves results in interference.

29. Destructive Interference: Exactly out of Phase Cancellation + Zero displacement

30. Constructive Interference: Reinforcement + Maximum Displacement In Phase

31. Interference Pattern The pattern formed by superposition of different sets of waves that produce mutual reinforcement in some places and cancellation in others. Superposition Principle of Wave

32. Standing Wave A stationary wave pattern formed in a medium when two sets of identical waves pass through the medium in opposite directions. lecture demos

33. Standing Wave Incident Wave V Reflected Wave V V Standing Wave V

34. Beats Sometimes, two waves with slightly different frequencies but the same amplitude can form the phenomenon known as beats. 15.11 Beats

35. Blue colored wave + green colored wave ==> red colored wave. Two waves with same amplitudes but slightly different frequencies.

36. Doppler Effect The shift in received frequency due to motion of a vibrating source toward or away from a receiver. 15.6 The Doppler Effect

37. Bow Wave The V-shaped wave made by an object moving across a liquid surface at a speed greater than the wave speed. (Since the source is moving faster than the wave speed, the wavefronts pile up.)

38. Shock Wave The cone-shaped wave made by an object moving at supersonic speed through a fluid. (Here, the source is moving faster than the wave speed, which is the speed of sound!!) (Super-sonic speed)

39. Sonic Boom The loud sound resulting from the incidence of a shock wave. (This is the result of the pile up of many wave fronts which produces a sonic boom)

40. Sonic Boom Piled up wave fronts produce a shock wave Plane

41. Twice the speed of sound - Mach 2 Wave front 1 unit Plane 2 units

43. The End of Chapter 19