1. Waves
Unit 11

2. Vibrational Motion
Wiggles, vibrations, and oscillations are an inseparable part of nature.
Much of what we see & hear is only possible because of vibrations and waves.
In this Unit we will explore vibrational motion and its relationship to waves.

3. Periodic Motion
A vibrating object is wiggling back and forth about a fixed position.
Like the mass on a spring, the mass moves up & down in a regular and repeated path.
In Physics, a motion that is regular and repeating is referred to as periodic motion.

4. Periodic Motion
Periodic motion – moving back & forth, vibrating, oscillating at repeated and regular intervals
What are some other examples of periodic motion?

5. Sinusoidal Nature of Vibration
Suppose that a motion detector was placed under the mass in order to detect the changes in position over time.
A position vs. time graph of the periodic motion would look like this…

6. Sinusoidal Nature of Vibration
Resting position
Characteristics:
Sine wave – vibrating back/forth about a fixed resting position
Periodic – regular repetitive motion
Dampening – energy is being dissipated; max & min decrease over time (not slowing down!)

7. Period Period – time is takes to complete 1 full cycle
Seconds / cycle
A full cycle of vibration can be thought of as movement from resting position (A) to its max height (B) down to its min position (D), and back to resting position (E).

8. Period
Using this graph, it is possible to determine to time it takes to complete a 1 full cycle or period.
Standard unit – second (s)
From position A to E it takes 2.3 seconds
If the motion is periodic (regular & repetitive) then it should take 2.3 s to complete any of the cycles!

9. Times at Beginning and End of Cycle (seconds)
Letters
Times at Beginning and End of Cycle (seconds)
Cycle Time (seconds)
1st
A to E
0.0 s to 2.3 s
2.3
2nd
E to I
2.3 s to 4.6 s
3rd
I to M
4.6 s to 6.9 s
4th
M to Q
6.9 s to 9.2 s
5th
Q to U
9.2 s to 11.5 s
6th
U to Y
11.5 s to 13.8 s

10. Amplitude
Amplitude – the max displacement of the mass from its resting position.
Dampening – energy is being dissipated; max & min decrease over time
Therefore the mass does not slow down, but it is the amplitude that decreases as time passes.
Amplitude is a reflection of the amount of energy possessed by the vibrating object. Larger the amplitude the more energy it has!

11. Frequency Frequency– number of complete cycles per unit of time.
Frequency = # of cycles / second
Standard units of frequency is Hertz (Hz)

12. Frequency
The concept of frequency is best understood if you associate it with its everyday meaning.
Frequency is a word we often use to describe how often something occurs.
You might say that you frequently check your or frequently talk with a friend.
Frequency refers to how often a repeated event occurs.

13. Frequency
A 256 Hz tuning fork makes 256 back & forth vibrations each second!
A 512 Hz tuning fork has an even higher frequency; you could say it vibrates faster at 512 cycles/second!
In comparing these 2 tuning forks its obvious that the one with the higher frequency has the lowest period.
256 Hz
512 Hz
*Higher the frequency the lower the period

14. Period vs. Frequency
Therefore we can say that period and frequency have an inverse relationship…in fact they are reciprocals of each other.
Period = time is takes to complete 1 full cycle (seconds / cycle)
Frequency = # of cycles per unit of time (cycles/sec.)

15. Period vs. Frequency
To better understand the distinction consider the following:
Tim Ahlstrom holds the record for hand clapping…
793 times in 60 seconds.
What is the frequency and what is the period of Tim’s hand clapping?
1 clap = 1 cycle
Frequency =
793 cycles / 60 sec. =
13.2 Hz
Period =
60 sec / 793 cycles =
seconds

16. Pendulum Motion

17. Pendulum Motion

18. Check for Understanding
Determine what point has the greatest…
Force of gravity?
Speed?
Potential energy
Kinetic energy
Total mechanical energy
Everywhere the same! C A C
Everywhere the same!

19. Check for Understanding
Us conservation of energy to fill in the blank
0.4
2.4
2.4

20. Waves

21. Waves Waves are everywhere! We encounter them on a daily basis…
Sound waves
Light waves
Radio waves
Microwaves
Water waves
We study waves because it gives us a glimpse into the nature of reality and helps us to understand how the physical world works.

22. Nature of Waves So waves are everywhere, but what makes a wave a wave?
What characteristics, properties, or behaviors are shared by waves?
Waves can be described as a disturbance that travels through a medium from one location to another.

23. Nature of Waves Lets consider a stretched slinky…
To introduce a wave to the slinky, the first particle is moved from is rest position creating a disturbance.
The particle might be moved up & down or forward & backward, but once moved, it returns to its rest position.
A single disturbance moving through a medium from one location to another is referred to as a pulse.
A repeating & periodic disturbance is called a wave.

24. Medium
What is a medium?
Medium is a substance or material that carries the wave (or disturbance) from one location to another.
The wave medium is not the wave nor does it make the wave; it merely transports the disturbance from here to there…
What is the medium in a slinky wave?
The slinky coils
In an ocean wave?
The ocean water
In a sound wave?
The air
In a stadium wave?
The fans

25. Particle to Particle Interaction

26. Energy Transport
When a waves moves through a medium, the individual particles of the medium are displaced from their rest position, but eventually returns to the original equilibrium position.
Therefore, a wave is said to transport energy and not matter!

27. Categories of Waves
One way to categorize waves is on the basis of the direction of the particles of the medium relative to the direction of the disturbance or wave.
Wave types:
Longitudinal waves
Transverse waves
Surface waves

28. Longitudinal Waves
A longitudinal wave is a wave in which particles of the medium move parallel to the direction of the wave.

29. Longitudinal Waves
A sound wave traveling through the air is a classic example of a longitudinal wave.
Sound is a pressure wave in the air particles causing them to vibrate back and forth starting a chain reaction in the air.

30. Longitudinal Waves
The direction of the vibrating air particles are parallel to the direction of the wave.
The wave is propagated through the air until the sound wave reaches the ear of the listener.

31. Transverse Waves
A transverse wave is a wave in which particles of the medium move perpendicular to the direction of the wave.

32. Surface Waves
A surface wave is a wave in which particles of the medium move in a circular motion.
Only the particles of the at the surface of the medium move.

33. Electromagnetic vs. Mechanical
Another way to categorize waves is by their ability or inability to transmit energy through a vacuum.
Electromagnetic waves (aka light) is a wave capable of transmitting energy through a vacuum (empty space) and do not need a medium to travel.

34. Long wavelength
Low frequency
Short wavelength
High frequency

35. Electromagnetic vs. Mechanical
Mechanical waves are not capable of transmitting energy through a vacuum.
They require a medium in order to transport their energy from one location to another.
A sound wave is an example of a mechanical wave and therefore incapable of traveling through a vacuum!
IN SPACE

36. Anatomy of a Transverse Wave
Crest – highest point of the wave
Trough – lowest point of the wave
Amplitude – max amount of displacement from rest (rest to crest)
Wavelength (λ) – length of one complete wave cycle (crest to crest)
A to E
D to G
B to F

37. Anatomy of a Longitudinal Wave
Compression – point on a longitudinal wave where the particles of the medium are most dense (compact).
Rarefaction – point on a longitudinal wave where the particles of the medium are least dense.
Wavelength (λ) – length of one complete wave cycle
A to C (compression to compression)
B to D (rarefaction to rarefaction)

38. Speed = Wavelength • Frequency
The Wave Equation
V= λf
Speed = Wavelength • Frequency
v – velocity or speed of a traveling wave
λ - wavelength in meters (m)
f – frequency in Hertz (Hz)

39. Behaviors of Waves

40. Law of Reflection
Reflection occurs when a wave bounces off an object, barrier, or surface.
Waves will always reflect in such a way that the angle at which they approach the barrier equals the angle at which they reflect off the barrier.
The angle of incidence is equal to the angle of reflection.

41. Refraction
Refraction is the bending of a wave caused by the change in speed of a wave as it passes from one medium to another.
Water waves travel fastest when the medium is deepest. Thus, if water waves are passing from deep into shallow water, they will slow down. The decrease in speed will be accompanied by a decrease in wavelength and direction change or bending of the waves.

42. Diffraction
Diffraction is the change in direction of waves as they pass through an opening or around a barrier in their path.

43. Interference What happens when two waves meet?
What effect will the meeting of the waves have upon the medium?
Will the two waves bounce off each other or will they pass through each other?
These questions involving the meeting of two or more waves pertain to the topic of wave interference.

44. Interference
Wave interference occurs when two or more waves meet or combine while traveling through the same medium.

45. Constructive Interference
Constructive interference is a type of interference where the waves combine so that the resulting wave is bigger than the original waves.
In phase

46. Destructive Interference
Destructive Interference is a type of interference where the waves combine so that the resulting wave is smaller than the largest of the original waves.
Out of phase

47. Check for Understanding
Categorize each labeled position along the medium as being a position where either constructive or destructive interference occurs.
G, J, M, & N – Constructive
H, I, K, L & O - Destructive

49. Check for Understanding
Twin water bugs Jimminy and Johnny are both creating a series of circular waves by jiggling their legs in the water. The waves undergo interference and create the pattern represented in the diagram. The thick lines in the diagram represent wave crests and the thin lines represent wave troughs. Several of positions in the water are labeled with a letter. Categorize each labeled position as being a position where either constructive or destructive interference occurs.
A & B – Constructive
C, D, E, & F - Destructive

50. Doppler Effect
The Doppler effect can be described as the effect produced by a moving source of waves in which frequency appears to increase or decrease relative to an observer.
If the source is moving towards an observer, frequency appears to increase.
If the source is moving away from an observer, the frequency appears to decrease.
It is important to note that the effect does not result from an actual change is frequency of the source.

51. Doppler Effect
The Doppler effect can be observed for any type of wave – water, sound, light, etc.
Low pitch
High pitch

52. Red Shift
The Doppler effect is of intense interest to astronomers who use the information about the shift in frequency of electromagnetic waves produced by moving stars in our galaxy and beyond in order to derive information about those stars and galaxies. The belief that the universe is expanding is based in part upon observations of electromagnetic waves emitted by stars in distant galaxies. Furthermore, specific information about stars within galaxies can be determined by application of the Doppler effect. Galaxies are clusters of stars that typically rotate about some center of mass point. Electromagnetic radiation emitted by such stars in a distant galaxy would appear to be shifted downward in frequency (a red shift) if the star is rotating in its cluster in a direction that is away from the Earth. On the other hand, there is an upward shift in frequency (a blue shift) of such observed radiation if the star is rotating in a direction that is towards the Earth.

53. Standing Waves http://www.youtube.com/watch?v=-gr7KmTOrx0

54. Standing Waves
A standing wave is a stationary wave confined to a given space.
The medium vibrates back & forth from positive displacement to negative displacement.
Points of the medium that never move (no displacement) are known as nodes.

55. Harmonics
Standing waves are created when the source wave interferes with the returning reflected wave.
Standing waves occur only at specific frequencies of vibration called harmonics.

56. Harmonics 2nd Harmonic 1st Harmonic 5th Harmonic 3rd Harmonic

57. Cymatics Cymatics is the study of visible sound and vibration.

58. Applications of Waves