Ch14 Waves

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Ch14 Waves
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Wave Types

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

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

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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
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• Transverse wave the medium vibrates
  perpendicularly to the direction of travel.

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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
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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.

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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.

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1
11
2
10
3
9
4
8
5
7
6
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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
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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
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Surface Wave

• Surface Waves Are a mixture of both parallel
  and perpendicular motion.

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Wave Pulse

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

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Hand Drawn Examples

• Transverse
• Longitudinal
• Pulse

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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)
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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)
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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)
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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
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Measures of a Wave

• Amplitude The maximum displacement from rest
  or equilibrium

Amplitude
.01 .02 .03 .04 .05 .06 .07 .08
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Wave Examples

• Can two waves can have the same wavelength and
  frequecy, but different amplitudes?

The greater the amplitude the greater the energy.
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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
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HW

• Read CH14
• Worksheet vibrations and Waves 1-8

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Wave Velocity
The velocity of a wave is the distance traveled
divide by the time it takes to move
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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?

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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?

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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.

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Wave Boundaries

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

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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.

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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?

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Waves at Boundaries
Low Density Medium
High Density Medium
Note Both amplitudes get smaller
Erect
Inverted
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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?

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Waves at Boundaries
High Density Medium
Low Density Medium
Erect Larger
Erect Smaller
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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.

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Wave Demos

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

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Practice Problems

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

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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.

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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
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Wave Superposition
The blue wave below represents the sum of the 2
other waves.
Destructive Interference
Constructive Interference
Nodes
Antinodes
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Wave Superposition
Nodes
Constructive Interference
Destructive Interference
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Interference of Sine Waves

• When two or more waves occur in close proximity
  to one another, they produce interference
  patterns.
• Constructive Interference
• Destructive Interference

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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

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Practice Problems

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

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Superposition of waves
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Practice Problems

• WS 14.1 9
• WS 14.3 3-5
• WS 14.5 1-6

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End Ch 14

• Chapter Quiz
• Moved standing waves to ch15

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Standing Waves

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

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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.

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Standing Waves

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

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Standing Waves

• Harmonics Standing wave that consist of more
  than one pulse

4th Harmonic
2nd Harmonic
1st Harmonic
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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.

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Harmonic Series in a string
1st Harmonic
2nd Harmonic
3rd Harmonic
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Reflection of Waves

• Normal
• Angle of incidence
• Angle of reflection
• Law of reflection

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Diffraction Waves

• Node
• Antinode
• demo

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Conservation of Energy Intro WS 2
PE
KE
PE
PE
PE KE
PE KE
KE
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superposition
A
A

B
B