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Ch14 Waves

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Title: Ch14 Waves


1
Ch14 Waves
2
Wave Types
  • Mechanical Waves require a medium (material) to
    propagate.
  • Water Rope
  • Springs Sound
  • 3 types of Mechanical Waves
  • Transverse
  • Longitudinal
  • Surface

3
  • Longitudinal Waves The medium vibrates parallel
    to the direction of the wave.

4
Longitudinal Waves
  • A Longitudinal A wave in which the vibration is
    in the same direction that the wave is traveling.
  • Notice how the atom in the box below never leaves
    the box even though the wave is obviously
    traveling to the right.

Animation courtesy of Dr. Dan Russell, Kettering
University
5
  • Transverse wave the medium vibrates
    perpendicularly to the direction of travel.

6
Transverse Mechanical Waves
  • A transverse wave is one in which the individual
    atoms or particles vibrate in a direction
    perpendicular to the direction of motion of the
    wave.
  • Notice how the atoms in the box below never leave
    the box even though the wave is obviously
    traveling to the right.

Animation courtesy of Dr. Dan Russell, Kettering
University
7
As the Wheel Turns
  • Watch how the sine function (which demonstrates a
    wave) traces out as a wheel turns.
  • The vertical axis represents horizontal position
    and the horizontal axis represents time.

8
Simple Harmonic Motion
  • Simple Harmonic Motion Motion caused by a linear
    restoring force that has a period independent of
    amplitude.
  • Period The time required to repeat one complete
    cycle
  • Amplitude Maximum displacement from equilibrium.

12
1
11
2
10
3
9
4
8
5
7
6
9
Transverse Wave
  • Transverse wave the medium vibrates
    perpendicularly to the direction of travel.
  • The wave travels horizontally. Any one point on
    the wave travels vertically

e.g. Pianos Guitar String
10
Standing Waves
  • Longitudinal Waves The medium moves parallel to
    the direction of the wave.
  • The wave travels horizontally. Any one point on
    the wave also travels horizontally.

Tuning Fork
Slinky
Sound
11
Surface Wave
  • Surface Waves Are a mixture of both parallel
    and perpendicular motion.

12
Wave Pulse
  • Wave Pulse A single disturbance that travels
    through a medium
  • A pulse can move in either direction

13
Hand Drawn Examples
  • Transverse
  • Longitudinal
  • Pulse

14
Measures of a Wave
  • Period (T) The shortest time interval during
    which motion repeats.

Period 4s
1 2 3 4 5 6 7 8

Time (s)
15
Measures of a Wave
  • Frequency (f) The number of complete vibrations
    per second.

5 cycles/s (Hz)
Number of vibration (cycles)
1 2 3
4 5
Note the X-axis is time
0.2 0.4 0.6 0.8
1.0 1.2 1.6 1.8

Time (s)
16
Measures of a Wave
  • Wavelength The shortest distance where
    the pattern of the wave repeats

.01 .02 .03 .04 .05 .06 .07 .08
Meters (m)
17
Measures of a Wave
  • Crest The highest point on a wave
  • Trough The lowest point on a wave

Crest
Trough
.01 .02 .03 .04 .05 .06 .07 .08
18
Measures of a Wave
  • Amplitude The maximum displacement from rest
    or equilibrium

Amplitude
.01 .02 .03 .04 .05 .06 .07 .08
19
Wave Examples
  • Can two waves can have the same wavelength and
    frequecy, but different amplitudes?

The greater the amplitude the greater the energy.
20
Waves
  • When these oscillations between two extremes are
    graphed wrt time, we see the following profile
    emerge.
  • The Wavelength (?) is the distance from the
    same point on two consecutive oscillations.
  • The Amplitude (A) is the maximum displacement
    from zero.
  • The Period (T) is the time between the same
    position on consecutive humps.
  • The Frequency (f) describes how often an
    oscillation occurs.
  • The high points on the wave are known as
    crests.
  • The low points on the wave are known as troughs.

A
0
-A
21
HW
  • Read CH14
  • Worksheet vibrations and Waves 1-8

22
Wave Velocity
The velocity of a wave is the distance traveled
divide by the time it takes to move
23
Example
  • A sound wave from a starters pistol is heard 100m
    down the track at the finish line.
  • How long did it take the starter to start the
    stop watch if he waited for the sound.
  • How long if he started the stopwatch when he saw
    the smoke?
  • How much faster do the runners times appear?

24
Example WS14.2 1
  • A sound wave produced by a clock chime 515m away
    is heard 1.5s later.
  • a) What is the speed of sound in air?
  • b) The sound wave has a frequency of 436Hz. What
    is its period?
  • c) What is its wavelength?

25
Wave Boundaries
  • What happens when a wave hits a boundary between
    two mediums?
  • Part of the wave is transmitted
  • Part is reflected
  • The amount that gets transmitted versus reflected
    depends on the difference between two mediums.

26
Wave Boundaries
  • When a wave is transmitted from less dense to
    more dense, the reflected wave is inverted.

27
Wave Boundaries
  • Reflection follow Newtons 3nd Law
  • The string pulls up on the wall
  • The wall pulls down on the string
  • The wall doesn't move
  • The string is reflected inverted.

28
Wave Boundaries example
  • A pulse is sent along a spring. The spring is
    attached to a light thread which is attached to a
    wall.
  • What happens when the pulse reaches the string?
  • Is the pulse reflected erect or inverted?
  • What happens when the transmitted pulse reaches
    the wall?
  • Is this pulse erect or inverted?

29
Waves at Boundaries
Low Density Medium
High Density Medium
Note Both amplitudes get smaller
Erect
Inverted
30
Wave Boundaries example
  • A pulse is sent along a light thread. The thread
    is attached to a spring which is attached to a
    wall.
  • What happens when the pulse reaches the spring?
  • Is the pulse reflected erect or inverted?
  • What happens when the transmitted pulse reaches
    the wall?
  • Is this pulse erect or inverted?

31
Waves at Boundaries
High Density Medium
Low Density Medium
Erect Larger
Erect Smaller
32
Wave Boundaries
  • The frequency of a wave being transmitted from
    one medium to another does NOT change.
  • e.g. If Im moving a string up and down, I dont
    change the velocity that I vibrate it.

33
Wave Demos
  • Spring to a fixed boundary (more dense)
  • Spring to a light string (less dense)
  • Light string to spring
  • Heavy spring to slinky.

34
Practice Problems
  • WS 14.2
  • s 2,3
  • WS 14.3
  • s 1,2
  • Page 296
  • s 5-8

35
Superposition of Waves
  • Principle of superposition The displacement of
    a medium caused by two or more waves is the
    algebraic sum of each wave.
  • Waves pass each other so the original wave
    continues unaltered.
  • Interference is the result of the superposition
    of two or more waves.

36
Wave Superposition
Constructive Interference
Antinode is the point of maximum displacement
(i.e., where amplitude is largest)
2 or more waves adding together to make a
larger wave
37
Wave Superposition
The blue wave below represents the sum of the 2
other waves.
Destructive Interference
Constructive Interference
Nodes
Antinodes
38
Wave Superposition
Nodes
Constructive Interference
Destructive Interference
39
Interference of Sine Waves
  • When two or more waves occur in close proximity
    to one another, they produce interference
    patterns.
  • Constructive Interference
  • Destructive Interference

40
Superposition of Waves
  • Constructive Interference Occurs when the
    displacements are in the same direction
  • Destructive Interference Occurs when the
    displacements are on opposite sides of
    equilibrium.
  • Show excel demo

41
Practice Problems
  • Sketch the resultant waveform when the center of
    the two waves are at the red boundary

42
Superposition of waves
43
Practice Problems
  • WS 14.1 9
  • WS 14.3 3-5
  • WS 14.5 1-6

44
End Ch 14
  • Chapter Quiz
  • Moved standing waves to ch15

45
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46
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47
Standing Waves
  • Standing Wave
  • Node
  • Antinode
  • Record these vocabulary terms and define their
    meaning using your text.

48
Standing Waves
  • Standing Wave has stationary nodes and
    antinodes. It is the results of identical waves
    traveling in opposite direction.
  • Node The medium is not displaced as the waves
    pass through
  • Antinode The displacement caused by interfering
    waves is largest.

49
Standing Waves
  • In order for a standing wave to exist, there must
    be an identical wave traveling in the opposite
    direction
  • Standing wave demo

50
Standing Waves
  • Harmonics Standing wave that consist of more
    than one pulse

4th Harmonic
2nd Harmonic
1st Harmonic
51
Standing waves
  • Fundamental Frequency The lowest frequency that
    creates a standing wave in a given medium.
  • Harmonics (overtones) frequencies with integer
    multiples of the fundamental frequency.
  • These frequencies make up the harmonic series.

52
Harmonic Series in a string
1st Harmonic
2nd Harmonic
3rd Harmonic
53
Reflection of Waves
  • Normal
  • Angle of incidence
  • Angle of reflection
  • Law of reflection

54
Diffraction Waves
  • Node
  • Antinode
  • demo

55
Conservation of Energy Intro WS 2
PE
KE
PE
PE
PE KE
PE KE
KE
56
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57
superposition
A
A

B
B
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