1. Warm-Up: January 30, 2012
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 initial, 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 from its equilibrium position

6. Example 1
How much force is needed to stretch a spring 25 cm if the spring constant is 105 N/m?

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

8. Energy of Springs
Stretching or compressing a spring also generates elastic potential energy
This is a different type of potential energy than the gravitational potential energy we’ve discussed

9. Example 2
A spring has a spring constant of 256 N/m. How far must it be stretched to give it an elastic potential energy of 48 J?

10. You-Try #2
A spring with a spring constant of 144 N/m is compressed by a distance of 16.5 cm. How much elastic potential energy is stored in the spring?

11. Resonance
Resonance occurs when small forces are applied at regular intervals to an object in periodic motion causing the amplitude to increase.
Examples include:
Pushing someone on a swing
Jumping on a diving board
Wind on the Tacoma Narrows Bridge

12. Warm-Up: January 31, 2012
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 force does the spring exert on the mass?
What is the weight of the block?
What is the elastic potential energy stored in the spring?

13. 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

14. 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

15. 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

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

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

20. Binder Quiz 15 minute time limit
You may use your binder, notes, notebook, and homework.
If you appear to be talking, you will receive a zero.
If you appear to be looking at anyone else’s papers, you will receive a zero.
If you appear to be allowing someone else to look at any of your papers, you will receive a zero.
Keep your quiz until time is up. They will all be collected at once.

21. 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

22. 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 compressions (or the distance between rarefactions)

25. Warm-Up: February 1, 2012
A man with a mass of 75 kg hangs from a spring that is attached to the ceiling, causing it to stretch 83 cm (after the oscillations stop). What is the spring constant of the spring?

26. 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.

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

28. 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

29. 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

30. 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

31. 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

32. Wavelength
Wavelength – Length of a cycle (distance between similar 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

33. Example 3
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

34. You-Try #3
Sound has a speed of 3100 m/s in copper. What is the wavelength of the wave from Example 3 after it crosses into a copper medium?
18 m

35. 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)

36. Warm-Up: February 6, 2012
A sound wave produced by a clock chime is heard 515 m away 1.50 s later.
What is the speed of the clock’s chime in air?
If the sound wave has a frequency of 436 Hz, what is the period of the wave?
What is the wave’s wavelength?

37. Homework Questions?

38. 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.

39. Superposition Examples

40. 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

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

43. Warm-Up: February 7, 2012
A wave has a frequency of 225 Hz. What is its period?
The wave changes medium from air to water. What happens to the period? (increase, remain constant, or decrease)

44. Homework Questions?

45. 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.

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

47. Assignment
Page 396 #31, 32, 33, 41, 42, 52, 56, 69, 71, 72, 76, 79, 81

48. Classwork Read Conceptual Physics chapter 25 (pages 372-386)
Answer review questions #1-20 on p

49. Warm-Up: February 13, 2012
List the five characteristics that are used to measure/describe waves.
Which of the above depend on the medium through which the wave is travelling?

50. Waves Worksheet Answers
energy
matter
transverse
longitudinal
surface
energy, formation
speed, wavelength

51. Waves Worksheet Answers
The speed of a wave is equal to its wavelength divided by its period.
If the frequency of a wave decreases while wave speed remains constant, the wavelength increases.
The wavelength of a longitudinal wave is the distance between compressions (or rarefactions). The wavelength of a transverse wave is the distance between crests (or troughs).

52. Waves Worksheet Answers