1. Waves

2. Waves are everywhere. Sound waves, light waves, water waves, stadium waves, earthquake waves, waves on a string, and slinky waves and are just a few of the examples of waves. Waves transport energy from one location to another. Waves are caused by vibrations Vibration (or oscillation) -- back-and-forth or up-and-down motion; a wiggle in time. Wave -- a disturbance that travels from one location to another; a wiggle in space and time. The medium is a substance or material that carries the wave.

3. Anatomy of a Sine Wave The parts of a wave include crest, trough, wavelength, amplitude, frequency and period The points A and F are called the CRESTS of the wave. crest This is the point where the wave exhibits the maximum amount of positive or upwards displacement trough The points D and I are called the TROUGHS of the wave. These are the points where the wave exhibits its maximum negative or downward displacement.

4. Anatomy of a Sine Wave The distance between the rest position (shown by the dashed line) and point A is called the amplitude of the wave. The amplitude is the maximum displacement that the wave moves away from its equilibrium (dashed line). The distance between two consecutive similar points (in this case two crests) is called the wavelength. The wavelength is also the length of the wave pulse. Amplitude Wavelength

5. Comparison of Characteristics of Waves These two waves have the same frequency but different amplitudes. These two waves have the same amplitude but different frequencies.

6. Frequency Hertz- a unit of frequency (named after Heinrich Hertz). 1 Hz = 1 vibration per second. Ex. 10 hertz means 10 vibrations per second. Radio stations operate on hertz frequencies. Pitch is the frequency of sound. Our limitations of hearing- 20 Hz to 20,000 Hz. – Ultrasonic (sound to hi frequency for us to hear) – Infrasonic (sound too low frequency for us to hear)

7. Wave Frequency and Period Frequency  measures how often something happens over a certain amount of time (# of waves/second). It is the number of complete waves that pass a point in a given period of time (usually a second). We can measure how many times a pulse passes a fixed point over a given amount of time. This will give us the frequency.

8. The Period of a Pendulum Period – time it takes for 1 complete wave to pass a point. Measured in sec. The motion of a pendulum and the motion of a mass on a spring can be described using a wave. The period of a pendulum is the time is takes for one full back and forth motion.

9. Wave Frequency and Period The period is also is the reciprocal of the frequency. Period = 1/ frequency T = 1 / f Frequency = 1/ period f = 1 / T

10. Wave Speed Wave speed is the distance the disturbance travels in a fixed amount of time. Wave speed can be determined from the product of the wavelength and the frequency velocity = wavelength x frequency v = f All waves traveling thru the same medium do so at the same speed!

11. Factors Affecting Speed Electromagnetic (light/radiant) waves travel at 3.0 x 10 8 m/s in air while sound travels in air at 3.0 x 10 2 m/s. 186,000 mi/s vs. 0.21 mi/s. Three factors that affect the speed of the wave in transferring energy are: – 1. Type of medium – 2. Temperature of medium – 3. State of matter of medium (solid, liquid, gas)

12. WaveTypes Waves which require a medium are mechanical waves, also known as compressional or longitudinal waves. Waves which do not require a medium are transverse waves, commonly electromagnetic waves.

13. Wave Motion Most waves we see travel through some substance or matter (medium), but weirdly enough, the medium doesn’t really travel just the energy. Examples of Mediums- 1.Air 2.Water 3.All phases of matter (s,l,g) **Not all waves require a medium though!**

14. Types of Waves Transverse wave - oscillations are transverse (perpendicular) (at right angles to) to the direction of motion Longitudinal (or Compression) wave - oscillations are in the direction of motion, or parallel to the direction of motion.

15. Transverse Waves Electromagnetic waves (light waves) are transverse. This is the same for stringed instruments.

16. Electromagnetic Waves

17. Visible Spectrum

18. Longitudinal Waves Also known as compressional waves or mechanical waves Medium compres- ses together or spreads out to form compressions and rarefactions

19. Longitudinal Waves Sound waves are longitudinal waves. They are produced by the vibrating air molecules.

20. Uses of Longitudinal Waves

21. Interference and the Superposition Principle Suppose two waves pass through the same medium. What happens? Wave interference is the phenomenon which occurs when two or more waves meet while traveling along the same medium. The superposition principle tells us how waves interact. The principle of superposition is sometimes stated as follows: When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location. Algebraic sum of two waves

22. Interference There are 2 types of interference: destructive and constructive. Destructive interference- this occurs when the crest of one wave overlaps the trough of another. This cancels the waves out. Constructive interference- occurs when the crests of two waves overlap causing them to join, this increases the amplitude.

23. Constructive Interference Constructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the same direction. The resulting displacement is greater than the displacement of the two interfering pulses alone.

24. Destructive Interference Destructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. The resulting displacement is less than the displacement of the two interfering pulses alone.

25. Wave Addition

26. Interference Beats – periodic changes in intensity of sound Inference in light produces light and dark patterns

27. Two Opposite Waves When the two opposite waves arrive at the same location, they cancel, destructively.

28. Interference Water waves from two oscillating sources show interference. Note light and dark areas where difference amounts of light pass thru the water. Ripple Tank

29. Boundary Behavior of Waves The behavior of a wave when it reaches the end of its medium is called the wave’s boundary behavior. When one medium ends and another begins, that is called a boundary. One type of boundary that a wave may encounter is that it may be attached to a fixed end. The reflected pulse has the same speed, wavelength, and amplitude as the incident pulse.

30. Standing Waves When a reflected wave interferes with an incident wave, a standing wave can form. Nodes are points of no motion Anti-nodes are points of maximum motion

31. Wave Reflection

32. Wave Behavior Now the we know the parts of a wave and how we describe and analyze them, we can look at wave behavior In the next section we will look at interference, the boundary behavior of waves, standing waves and the Doppler Effect. The Doppler Effect

33. The Doppler Effect is the apparent change in frequency of a wave due to relative motion between source and observer. As the sound move toward the observer, the apparent frequency decreases, the waves get compressed. As the sound moves away from the observer, the apparent frequency increases, the waves get “stretched out” A sound wave frequency change is noticed as a change in pitch.

34. Doppler Shift for Light

35. Doppler and Line of Sight We are only sensitive to motion between source and observer ALONG the line of sight.

36. Shock Waves When speed of object generating waves surpasses speed of waves in that medium, shock wave results

37. Shock Waves The more the source exceeds the wave speed the narrower the V

38. Wave Reflection Normal line (perpendicular to plane surface ) bisects incoming and outgoing ray to determine angle of incidence or angle of reflection

39. Wave Reflection Law of reflection – angle of incidence = angle of reflection

40. Wave Reflection From a single point

41. Wave Reflection From a concave surface

42. Wave Reflection Acoustics of room design is very interesting. Need some reflections to “liven” the room. Too many reflections and the sound gets mushy. Look in a concert hall or auditorium to see the different sound treatments

43. Wave Behavior- Refraction Refraction- the bending of waves in various angles as it goes from 1 medium to another.

44. Refraction Waves traveling from the deep end to the shallow end can be seen to refract (i.e., bend), decrease wavelength (the wavefronts get closer together), and slow down (they take a longer time to travel the same distance).

45. Refraction

46. Wave Behavior Diffraction Diffraction -- object causes a wave to change direction and bend around it. The amount of bending depends on the size of the obstacle and the wavelength of the wave. If an obstacle is larger than the wavelength, the waves do not diffract much.

47. Natural Frequencies Objects have “natural” frequencies based on their size and structure Guitar strings are an example Timpani heads Air columns

48. Forced Vibrations Can externally impose a vibration on an object Guitars and violins and pianos Set the wood into motion at the frequency of the string This provides a larger surface to interact with the air Harp vs. Piano

49. Resonance When the forced vibration matches a natural frequency we get a “resonance” condition Think about a swing on a playground You go high when you pump the swing at its natural vibration frequency Other examples: – Sympathetic vibrations in tuning forks – Famous Tacoma Narrows bridge collapse

50. Resonance Swinging a child in a playground swing is an easy job because you are helped by its natural frequency. But can you swing it at some other frequency?

51. Opaque, Transparent, Translucent Wave behaviors cause objects to appear differently.

52. Reflection and Refraction

53. Harmonics There are a variety of patterns by which the guitar string could naturally vibrate; each pattern is associated with one of the natural frequencies of the guitar strings.

54. Sources Conceptual Physics by Paul Hewitt www.physicsclassroom.com pls.atu.edu/physci/physics/people/robertson/courses/phsc10 13/PHSC1013-Waves.ppt – Waves and Vibrations -Physics: Mr. Maloney www.drake.edu/artsci/physics/Lecture_14_3-4-2004.ppt https://bba-physics.wikispaces.com/file/view/Waves2.ppt https://bba-physics.wikispaces.com/file/view/Waves2.ppt www.knott.k12.ky.us/schools/teachers/nritchie/waves%20go od%20copy.ppt

55. Characteristics of ALL waves! Crest (compression) Trough (Rarefactions) Wavelength Amplitude Frequency Wave Speed- V= f

56. Sound in warm air near the ground doesn’t seem to carry well because the warm air causes the sound to bend away from the ground. This is just the opposite for cool air.

57. Wave Questions 1)Rhonda sends a pulse along a rope. How does the position of a point on the rope, before the pulse comes, compare to the position after the pulse has passed? 2)Why don't incoming ocean waves bring more water on to the shore until the beach is completely submerged? 3)In order for a medium to be able to support a wave, the particles in the wave must be a) frictionless. b) isolated from one another. c) able to interact. d) very light. 4)A transverse wave is transporting energy from east to west. How will the particles of the medium will move? 5)A wave is transporting energy from left to right. The particles of the medium are moving back and forth in a leftward and rightward direction. This type of wave is known as a _______________.

58. More Wave Questions 6) In the diagram above, the wavelength is given by what letter? 7) In the diagram above, the amplitude is given by what letter? 8) A wave has an amplitude of 2 cm and a frequency of 12 Hz, and the distance from a crest to the nearest trough is measured to be 5 cm. Determine the period of such a wave. 9) A tennis coach paces back and forth along the sideline 10 times in 2 minutes. The frequency of her pacing is ________. 10) A pendulum makes 40 vibrations in 20 seconds. Calculate its period? 11) Mac and Tosh are resting on top of the water near the end of the pool when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave. 12) A marine weather station reports waves along the shore that are 2 meters high, 8 meters long, and reach the station 8 seconds apart. Determine the frequency and the speed of these waves.