1. Warm-Up: February 17/18, 2016
Where do we encounter waves? Write down all the examples of waves that you can think of.

2. Vibrations and Waves
Chapter 14

3. Periodic Motion A periodic motion repeats in a regular cycle.
Examples include:
Pendulums (such as on a grandfather clock)
A mass at the end of a spring
Vibrating guitar string
The period is the amount of time for one complete cycle.
The amplitude is the maximum amount that the object moves from its equilibrium position

4. Periodic Motion Graph x

5. Springs
When you stretch or compress a spring, the spring exerts a force to return it to its equilibrium position.
The amount of force is given by Hooke’s Law
where 𝑘 is the spring constant (a property of the individual spring)
and 𝑥 is the distance the spring is displaced from its equilibrium position

6. You-Try #1
How much force is needed to compress a spring 12 cm if the spring constant is 84 N/m?

7. Energy of Springs
Stretching or compressing a spring also generates elastic potential energy

8. You-Try #2
How far must a spring with a spring constant of 444 N/m be compressed to produce an elastic potential energy of 8.25 J?

9. Assignment
Read Chapter 14
Page 378 #1-5

11. Today’s Lab – Feb. 19, 2016 You will be assigned to a group.
Your group’s goal is to experimentally show how each of the following affect the period of an oscillation (the time it takes to complete one cycle).
The mass at the end of the string
The length of the string
The angle of oscillation (keep ≤45° from vertical)
Materials allowed:
String (and scissors to cut the string)
Masses
Rulers/Metersticks/Protractors
Stopwatch (cell phone)
Tape
Be sure to record everything (procedures and data)

12. Lab Roles Leader: Procedures recorder: Data recorder:
Keep group on task
Collect and return supplies
Determine who performs each part of the lab (timing, etc.)
Procedures recorder:
Write down everything that your group does (whether it ends up working or not)
Data recorder:
Write down all data
Helper (2nd period only):
Fill in for any absent group member(s)
Assist group members as needed.

13. Lab Groups – Period 3 Leader Procedures Recorder Data Recorder Group 1
Le, Dylan
Luu, Justin
Suri, Anirudh
Group 2
Kim, Younghoon
Harris, Samantha
Remigio, Allexa
Group 3
Wong, Gracie
Manam, Abhinav
Bantigue, Alanna
Group 4
Yue, Linton
Sitapati, Kedar
Roos, Spencer
Group 5
Nguyen, Austin
Bey, Jack
Swartz, Erika
Group 6
Herring, Grace
Ton, Tyler
Townsend, Jaren
Group 7
Kim, Sean
Clarke, Jacob
Wadhwa, Sahil
Group 8
Marasigan, Emmanuel
Howo, Michael
Jewell, Katherine
Group 9
Hill, Megan
Julazadeh, Hana

14. Nagelvoort, Christopher
Lab Groups – Period 2
Leader
Procedures Recorder
Data Recorder
Helper
Group 1
Bhushan, Somil
Sandfer, Connor
Gupta, Mihir
Kye, Johanna
Group 2
Kapoor, Pia
Laudenslager, Alexis
Wedge, Lauren
Pennington, Julia
Group 3
Lodge, Grace
Lee, Rudolph
Hagstrom, Erik
Folkl, Julia
Group 4
Nguyen, Haley
Rao, Ananya
Obermiller, Andrew
Nguyen, Wendy
Group 5
Thomas, Zoe
Almond, Amber
Hardisty, Sabrina
Sharma, Amitesh
Group 6
Nagelvoort, Christopher
Andersen, Blake
Calkins, Nicholas
Castaneda, Ernesto
Group 7
Yang, Jerry
Kwan, Crystal
Imler, Carson
Padmanaban, Sneha
Group 8
Jones, Cameron
Waldman, Philip
Brana, Jennifer

16. Warm-Up: February 22, 2016
A spring is compressed by a 22 N force, giving it a potential energy of J.
What is the spring constant of the spring?
How far was the spring compressed?

17. Lab Conclusions How does mass/length/angle affect the period?
No effect?
Linear effect? If so, what is the equation of the line?
Non-linear effect? If so, what function is it (exponential, logarithmic, quadratic, etc.)?
Combine your results to write an equation for the period in terms of mass, length, and angle.
The equation may also include constants.
Compare your experimental result with the textbook equation. Why are they different?

18. Lab Report Must be typed One copy per lab group
Graphs must be computer generated (such as with Excel, Google Docs, etc.)
Procedures recorder should type procedures
Data recorder should type raw data
Group should work together on:
Introduction
Graphs and data analysis
Conclusions

19. Finish the Lab You will be assigned to a group. Materials allowed:
Your group’s goal is to experimentally show how each of the following affect the period of an oscillation (the time it takes to complete one cycle).
The mass at the end of the string
The length of the string
The angle of oscillation (keep ≤45° from vertical)
Materials allowed:
String (and scissors to cut the string)
Masses
Rulers/Metersticks/Protractors
Stopwatch (cell phone)
Tape
Be sure to record everything (procedures and data)

21. Warm-Up: February 23, 2016
A small marble 𝑚=2.75 g is pressed down on a vertical spring 𝑘=38 N m , causing the spring to compress 3.0 cm from its equilibrium position. The marble is released, and the spring shoots it straight up into the air. How high above the spring’s equilibrium position does the marble reach?

22. The Simple Pendulum Small-diameter mass, called the pendulum bob
String has negligible mass, but strong enough to not stretch appreciably
Undergoes simple harmonic motion if 𝜃<15°

23. Period of Simple Pendulum
Period is the amount of time for one cycle.
Represented by a capital 𝑇.
Measured in seconds, s.

24. Frequency 𝑓= 1 𝑇 Frequency is the reciprocal of period.
Represented by lower case 𝑓.
Measured in Hertz, Hz
1 Hz = 1/s
𝑓= 1 𝑇

25. Period of Simple Pendulum
Does not depend on mass.
Does not depend on amplitude (for 𝜃<15°)
Can be finely adjusted, and can make excellent clocks.
Can also be used to solve for 𝑔.

26. You-Try #3
What is the acceleration due to gravity in a region where a simple pendulum having a length of cm has a period of s?

27. Think-Pair-Share
What is the effect on the period of a simple pendulum if you double its length?

28. You-Try #4
What is the length of a pendulum that has a period of s? Let g=9.80 m/s2.

29. You-Try #5
The pendulum on a cuckoo clock is 5.00 cm long. What is its frequency? Let g=9.80 m/s2.

30. Resonance
Resonance occurs when small forces are applied at regular intervals to an object in periodic motion causing the amplitude to increase.

31. Think-Pair-Share
Write down as many examples of resonance that you can think of.

32. Resonance Examples include: Pushing someone on a swing
Jumping on a diving board
Wind on the Tacoma Narrows Bridge

33. Assignment Read Section 14.1 Page 379 #6-8 Page 380 #9-13

35. Warm-Up: February 24/25, 2016
A spring has a spring constant of 125 N/m. It is attached to the ceiling and a block is attached to the bottom. The spring is stretched 20.0 cm.
Draw a free body diagram of the block.
What is the magnitude of the force that the spring exerts on the block?
What is the weight of the block?
What is the elastic potential energy stored in the spring?

36. Homework Questions?

37. Waves
A wave is a disturbance that carries energy through matter or space
A wave usually does NOT transfer mass, only energy
A wave pulse is a single bump or disturbance. Most waves are a series of wave pulses.
Two main types of waves:
Mechanical waves – travel through matter
Electromagnetic waves – do not require matter, can travel through a vacuum

38. Mechanical Waves Examples include:
Water waves
Sound waves
Waves on a rope
Waves on a spring
Mechanical waves require a medium (matter) through which they propagate (travel).
Three main categories:
Transverse Waves
Longitudinal Waves
Surface Waves

39. Transverse Waves
A transverse wave is one that vibrates perpendicular to the direction of the wave’s motion
A wave on a rope is an example of a transverse wave
Simulation

40. Parts of a Transverse Wave
Crest – The highest point
Trough – The lowest point
Amplitude – The maximum displacement of the wave
The higher the amplitude, the greater the amount of energy transferred.
Wavelength – The distance between consecutive crests (or the distance between consecutive troughs)

41. Think, Pair, Share
Identify which point(s) correspond with each of the following: crest, trough, amplitude, wavelength

44. Longitudinal Waves
A longitudinal wave is one whose disturbances are in the same direction as (parallel to) the direction of the wave’s motion
Sound waves are longitudinal
Waves from a compressed
spring are longitudinal

45. Parts of a Longitudinal Wave
Compression – A dense part of a longitudinal wave
Rarefaction – A low density part of a longitudinal wave
Wavelength – The distance between consecutive compressions (or the distance between consecutive rarefactions)

47. Surface Waves
Surface waves are waves with characteristics of both transverse and longitudinal waves.
Ocean waves are a prime example of surface waves.
The paths of individual particles are circular.

48. Measuring Waves
The following are all used to measure and/or describe waves:
Wave Speed
Amplitude
Period
Frequency
Wavelength

49. Wave Speed Wave Speed – The distance a wave travels per unit time
Represented by a lower case 𝑣
Measured in meters per second, m/s
Depends on the medium through which the wave is travelling

50. Amplitude
Amplitude – The maximum displacement of a wave from its at-rest position
Represented by a capital 𝐴
Measured in meters, m
Depends on how the wave was generated
Does not depend on the wave speed or the medium
More work must be done to generate larger amplitude waves.
Waves with larger amplitudes transfer more energy

51. Period Period - the amount of time for one complete cycle/oscillation
Represented by a capital 𝑇
Measured in seconds
Depends only on the wave source
Does not depend on the wave speed
Does not depend on the medium

52. Frequency Frequency – The amount of cycles/oscillations per second
Represented by a lower case f
Measured in Hertz, Hz
Depends only on the wave source
Does not depend on the wave speed
Does not depend on the medium

53. Wavelength
Wavelength – Length of a cycle (distance between consecutive corresponding points)
Distance between crests (or troughs) of a transverse wave
Distance between compressions (or rarefactions) of a longitudinal wave
Represented by Greek letter lambda, 𝜆
Measured in meters

54. You-Try #6
Sound waves travel approximately 340 m/s in air. What is the wavelength of a sound wave that has a frequency of 170 Hz?
2.0 m

55. You-Try #7
Sound has a speed of 3100 m/s in copper. What is the wavelength of the wave from You-Try #6 after it crosses into a copper medium?
18 m

56. Assignments Read Section 14.2 Page 386 #15-25 Read Section 14.3

57. Warm-Up: February 26, 2016
A sound wave produced by a clock chime is heard 848 m away 2.50 s later.
What is the speed of the clock’s chime in air?
If the sound wave has a frequency of 375 Hz, what is the period of the wave?
What is the wave’s wavelength?

58. Homework Questions?

59. Wave Reflection
What happens when a wave reaches the end of its medium?
When the incident wave reaches the end of its medium, some or all of the energy is reflected back as a reflected wave.
Some reflected waves are inverted, such as waves on a rope with a fixed end (as in the simulation)

60. Superposition
The principle of superposition states that the amplitude of passing wave pulses is additive.
If pulses are on opposite sides, one amplitude is negative (adding a negative  subtracting)
The result of superposition is called interference.

61. Superposition Examples

62. Standing Waves
Interference can cause standing waves, which appear to not propagate.
Example: Rope moves up and down, but no wave pulses move to either side.
The nodes are points that do not move.
The antinodes are the points that move the most.
Simulation: Amplitude=20, Frequency=30, Damping=0, Tension=high-1

64. Standing Waves in Music
Stringed instruments depend on standing waves to make music.
These standing waves are called harmonics.

65. Waves in Two Dimensions
Often represented by a wave front, a line that represents a wave crest.
Waves move perpendicular to the wave front, often represented by a ray.

66. Reflection of 2-D Waves
The law of reflection states that the angle of incidence equals the angle of reflection

67. Assignment Read Section 14.2 Page 386 #15-25 Read Section 14.3