Waves

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 • 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!) Resting position

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!

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 email 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 = 0.0757 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 0 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 wavenor does it make the wave; it merely transports the disturbance from here to there… • What is themedium in a slinkywave? 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. 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 • Constructiveinterference 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.