Waves

1
Waves

• Harmonic Motion

2
Periodic Motion

• Repeat in a regular cycle
• Examples
• Period T
• Time required to complete one cycle
• Frequency f
• Cycles that occur in one second
• Frequency is in hertz, Hz, which is 1/sec

3
Periodic Motion

• Springs as periodic motion
• Always tries to return to equilibrium
• Hookes Law
• F-kx
• Potential Energy in a Spring
• PEsp1/2 kx2

4
Periodic Motion

• Pendulum as simple harmonic motion
• Always tries to return to equilibrium

Distance from equilibrium as a function of time
http//www.phy.ntnu.edu.tw/ntnujava/index.php?topi
c11
5
Wave Properties

• Types of Waves and Measuring Waves

6
Wave Properties

• Amplitude

Maximum distance from equilibrium
7
Wave Properties

• Peak-to-Peak Amplitude

Distance from Crest to Trough (or from low peak
to high peak)
8
Wave Properties

• Wavelength ?

9
Wave Properties

• Period/frequency
• Essentially the same variable, just inverted
• T 1/f Seconds per cycle
• f 1/T Cycles per second
• (just remember frequency always has 1 sec as the
  denominator)

Cycles per second and seconds per cycle Crash
10
Wave Properties

• Phase
• A way to describe the relationship between two
  points on waves

¼ of the distance from the other wave
¼ x 360 90 degrees out of phase
11
Wave Properties

• Equations
• Frequency f 1/T
• Wavelength ? v/f
• flambda v f ? (speed or velocity of a wave)

¼ wavelength
meters
x(meters)
t(seconds)
12
Wave Properties
13
(No Transcript)
14
Problems

• In Class
• Pg 397
• 64, 65, 66, 67, 68, 69, 71, 73, 75, 76, 77, 79,
  80
• Homework
• Pg 398
• 81, 82, 88, 89, 90, 97, 102

15
Wave Behavior

• Multiple waves, multiple boundaries

16
Wave Behavior

• Multiple waves can exist in the same place at the
  same time.
• Multiple particles cannot exist in the same place
  at the same time
• Note This is where the dilemma occurs when
  waves and particles are not clearly separated.

17
Boundaries

• Incident waves
• Waves that strike the boundary
• Reflected waves
• Waves that return from the boundary

Boundary
18
Reflected Waves

• Fixed/Rigid
• Inverted reflection
• Loose
• Non-inverted reflection
• No end
• No reflection
• Reflected waves do not change speed (ever).
  Speed is a function of the medium.

http//www.phy.ntnu.edu.tw/ntnujava/index.php?topi
c11
19
Principle of superposition

• The displacement of the medium caused by two or
  more waves is the algebraic sum of the
  displacements caused by the individual waves.
• Interference The result of the superposition of
  two or more waves.

20
Interference

• Constructive
• Result is bigger
• Destructive
• Result is smaller

21
Interference

• Node Has zero displacement, does not move at
  all.
• Antinode Has maximum displacement.

What is the pattern? ( of nodes vs. antinodes)
22
Standing Wave

• Standing wave Appears to be standing still. Is
  the interference of two or more waves.

23
Waves in two dimensions
24
Waves in two dimensions

• Wave front A line that represents the crest or
  peak of a wave in 2D. Can be any shape (e.g.
  straight, circular, etc.).

25
Law of reflection

• Law of reflection
• The angle of incidence is equal to the angle of
  reflection

26
Refraction

• Refraction The change in the direction of waves
  at the boundary between different media.
• Examples are echoes and rainbows

27
Rules to Remember

• Speed of a wave only changes when the medium
  changes (i.e. water depth changes or wave crosses
  a boundary into a different medium).
• Speed will not change because of wavelength or
  frequency
• Frequency only changes when the source changes
• Frequency will never change when the wave crosses
  a boundary

28
Read the Graph

• Maximum Speed, Zero Force, No Acceleration
  Equilibrium Point
• Maximum Displacement, Maximum Amplitude, Maximum
  Force, Zero Velocity, No Motion

29
Things you need to know

• EPEKE
• Work is Energy - work done is equivalent to the
  change in potential energy
• All lengths need to be in meters

30
(No Transcript)
31
Problems

• Consider a 10.0-kg pendulum clock that has a
  period of 1s on Earth. If the clock is moved to a
  location where it weighs 98 N, how many minutes
  will the minute hand move in 1 h?
• Write the equation for Earth
• Write the equation for the new location
• Set up the ratios

32
Problems

• Spring A with a spring constant of 253 N/m is
  stretched by a distance of 18.0 cm when a block
  is suspended from its end. An object is suspended
  from another spring B with a spring constant of
  169 N/m. If the elastic potential energy in both
  the springs is the same, how far does spring B
  stretch?
• Two parts
• Find k with F-kx
• Compare with PE ½ kx2

33
Problems

• A 150-g object subject to a restoring force F
  kx is undergoing simple harmonic motion. Shown
  below is a plot of the potential energy, PE, of
  the object as a function of distance, x, from its
  equilibrium position. The object has a total
  mechanical energy of 0.3 J.

a. What is the farthest the object moves along
the x-axis in the positive direction? Explain
your reasoning. b. What is the objects potential
energy when its displacement is 4.0 cm from its
quilibrium position? c. Determine the objects
kinetic energy when its position is x 8.0
cm. d. What is the objects speed at x 0.0 cm?
34
Answer

• a. Answer 10.0 cm or 0.100 m. The total
  mechanical energy is E 0.3 J, and total
  mechanical energy is given by E KE PE. Since
  the maximum potential energy cannot be greater
  than the total mechanical energy, the maximum
  potential energy is also 0.3 J. From the graph,
  PE 0.3 J at x 10.0 cm. Hence the maximum
  possible position in the x-direction is 10.0 cm
  or 0.100 m. The particle stops at this point
  (i.e. the kinetic energy KE 0 at this point)
  because all of the energy is in the form of
  potential energy.
• b. PE 0.05 J
• Method 1
• Read off the value from the graph PE 0.05 J
• Method 2
• Since the restoring force is given by Hookes law
  F kx, we can use the following equation for
  the potential energy of simple harmonic motion
• PEsp ½ kx2
• The maximum value of potential energy is PEmax
  0.3 J. This occurs at a distance of xmax 10.0
  cm 0.100 m. Use these values to determine the
  value of the spring constant k
• k 2PEmax/(x max2) 2(0.3J)/(0.100m)2 60M/n
• Then, to determine the value of PE at x 14.0 cm
  0.040 m
• PEsp ½ kx2 ½ (60N/m)(0.040m)2 0.05J

35
Answer

• c. 0.1 J
• Method 1
• Read off the value from the graph PE 0.2 J
  The total mechanical energy is the sum of kinetic
  energy and potential energy
• E KE PE
• Find the kinetic energy
• KE E PE 0.3 J 0.2 J 0.1 J
• Method 2
• Use the value of the spring constant k found in
  part b
• k 60 N/m
• Determine the value of PE at x 28.0 cm 20.080
  m
• PEsp ½ kx2 (60N/m)(20.080m)2 0.2J
• Then, find the kinetic energy
• E KE PE
• KE E PE
• 0.3 J 0.2 J 0.1 J
• d. 2 m/s
• At x 0.0cm,PEsp ½ kx2 0
• E KE PE KE 0
• so

36
Problem

• Read the graph
• Given the incident wave travels at 1.0m/s
• How much time has passed in graph b?
• How far has the transmitted wave traveled in that
  time?
• What is the velocity of the transmitted wave in
  graph b?

37
Problem

• Given 3 nodes and 2 antinodes in a 2-meter span
  
• What happens when the frequency is doubled?
• What is the wavelength?
• Does the velocity change if the frequency
  changes?
• Write an equation relating the first frequency
  and wavelength to the second frequency and
  wavelength.

38
Wave table or Ripple tank
39
Problems

• In Class
• Pg 391
• 27, 28, 29, 30,
• Homework
• Pg 398
• 84, 85, 86, 87, 91, 93

40
Boundaries

• Fixed
• Loose
• No end
• Incident waves
• Reflected waves Do waves slow down after
  reflection?
• Principle of superposition
• Wave interference
• Node
• Antinode
• Standing waves
• 2-D reflection
• 2-D refraction
• Normal
• Law of reflection angle of incidence is equal
  to angle of reflection

http//phet.colorado.edu/simulations/sims.php?sim
Wave_on_a_String
41
Your Topic Goes Here

• Your subtopics go here

42
Transitional Page
43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
(No Transcript)
47
(No Transcript)
48
(No Transcript)
49
Is it hot in here?
50
Elements

• www.animationfactory.com

51
(No Transcript)
52
(No Transcript)