2/22 Good morning!

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2/22 Good morning!

• Friday we took the Circuit Test
• Make Ups today tomorrow after school
• Corrections/retakes through Wednesday
  afterschool.

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Pick up notes packet and warm up sheet
2/23 Warm Up 1 What is the unit for force?
For displacement?
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If you were absent yesterday, pick up notes, new
warm up Sheet, and SHM WS I
Begin working on SHM WS I
3/17 Warm Up 2 What is the definition of
period? of frequency?
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3/18
SHM WS I and WS II due end of class today
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• 3/19 Lab Today!

Warm Up 3 A pendulum swings back and forth 27
times in 10 seconds. What is its period?
Turn is SHM WS I and WS II to blue sorter. Make
sure your name is on it and title them SHM I and
SHM II. Classes that met yesterday already did
this.
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3/20
Warm Up 4 Determine current in a wire that has a
resistance of 10 ohms and a 9-volt electrical
source.
Yesterday we did the pendulum lab. Make up is in
the brown mailbox. SHM WSI and SHM WSII were due
yesterday as well.
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3/23 Pick up SHM WS III
Friday we began the notes on waves
Warm Up 5 A wave is 3 meters from crest to
trough. What is its amplitude?
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3/24 FIRST Finish Notes No warm up today
Yesterday I collected warm ups You were assigned
SHM Waves WS III Today finish WSIII and work on
Review Quiz tomorrow, test Thursday
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3/25 Get a calculator No warm up today-Look over
your notes for quiz
Quiz today, test tomorrow
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3/26 Get a calculator And formula chart. Place
notes ONLY at back of room.
Test today Turn in SHM III to Sorter now
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Refer to the formula for calculation of period

• If one knew the length and period, what could one
  calculate?
• GRAVITY!!!!

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From test adjust and use as a warm up

• A water wave with the speed of 5 m/s and a
  frequency of 10 waves per minute hits the shore.
  If you are 200 m out from shore how many waves
  will you see between you and the shore?

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Formulas
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What do the following all have in common?

• Swing, pendulum, vibrating string

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They all exhibit forms of periodic motion.

• Periodic Motion
• When a vibration or oscillation repeats itself
  over the same path

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Simple _________ Motion (SHM)
Harmonic

• A specific form of periodic motion in which the
  restoring force is proportional to distance from
  the equilibrium position.

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Objects that exhibit SHM

• Spring Systems
• Pendulums
• Circular Motion
• Waves
• Sound, Light, Pressure

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Definitions

• Period Time required for one complete cycle
• T (sec/cycle) measured in seconds
• Frequency - Number of complete cycles in a
  period of time (
• f (cycle/sec) measured in Hertz
• Amplitude Displacement from the equilibrium
  position. It is a measure of energy

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Definitions

• Equilibrium Position - The center of motion the
  place at which no forces act.
• Displacement - The distance between the center
  (equilibrium position) and location of the
  spring, pendulum, or wave at any time.

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Example 1

• A fishing bobber moves up and down 24 times in 1
  minute.
• A What is its period?
• B What is its frequency?
• C What is the relationship
• between Period and
• Frequency?

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Example 1

• A What is its period?
• T sec/cycle
• T 60 sec/ 24 bobs
• T 2.5 seconds

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Example 1

• B What is its frequency?
• f Cycles/Sec
• f 24 bobs/60 sec
• f 0.4 Hz

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Example 1

• C What is the relationship
• between Period and
• Frequency?
• T sec/cycle f Cycles/Sec
• They are reciprocals of each other!
• 1/0.4 Hz 2.5 sec
• 1/2.5 seconds 0.4 Hz

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SHM and Springs

• Demo Vertical spring
• What is the natural state for the spring?
• What causes it to be stretched or compressed?
• What causes it to return to its natural state?

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SHM and Springs

• Compare various springs
• How are they different?
• What does that mean?

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Horizontal Springs

• It has a mass of some kind attached to a spring.
• This spring is stretched and released. This
  causes the entire system to oscillate. (move back
  and forth)

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Springs

• So the equation for force of a spring is as
  follows
• FS kx
• (Hookes Law)
• FS the force supplied by the spring
• K the spring constant (depends on how the
  spring is made)
• x displacement of the spring from its
  equilibrium position

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Hookes Law

• Fspring magnitude of the distorting or
  restoring force in Newtons
• K spring constant or force constant (stiffness
  of a spring) in Newtons per meter (N/m)
• x displacement from equilibrium in meters

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If time

• Simple harmonic motion - Physics Flash Animations

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Application in Engineering and design

• beyond springs and rubber bands
• Chairs
• Floors
• Anything that flexes and provides an upward
  support force

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Example 2

• I have a slinky with a spring constant of 130
  N/m. With what force do I need to pull it to
  stretch the slinky from its equilibrium position
  for the following displacements?
• 0.1m
• 0.5 m
• What is the relationship between Force and
  displacement?
• How would the required force (to displace the
  mass 0.1m) change if the spring constant was
  doubled?

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Example 2

• I have a slinky with a spring constant of
  130 N/m. With what force do I need to pull it in
  order to stretch the slinky from its equilibrium
  position for the following displacements?
• 0.1 m Fs (130N/m) (0.1m) 13 N
• 0.5 m Fs (130N/m) (0.5m) 65 N
• What is the relationship between Force and
  displacement? Directly Proportional
• How would the required force (to displace the
  mass 0.1m) change if the spring constant was
  doubled? Fs (260N/m) (0.1m) 26 N
• Spring Constant is directly proportional to F

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Period on a Spring

• If we stretch a spring with a mass and release
  it, it will oscillate.
• This is SHM!
• What is the period
  of this
• Motion?

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Period on a Spring

• The period of a spring system is given by the
  equation below
• T the period of motion
• m Mass of the body attached
• k spring constant

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Period

• What is the relationship between mass and period
  of a spring?
• What is the relationship between spring strength
  (Think spring constant) and period of a spring?
• Remember that period is always in seconds!

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Example 3

• What is the mass of my car if the shocks have a
  spring constant of 6000 N/m and it oscillates
  with a period of 2 seconds when I hit a bump in
  the road?
• m (6000 N/m)(2 s)2/4p2
• m 607.9 kg

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• What is the difference between period and
  frequency?

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Formulas Calculating Period and Frequency
T period or time for one revolution or cycle
(sec) f number of revolutions or cycles per
second (Hz or sec-1)
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Lets take a jump!

• http//departments.weber.edu/physics/amiri/directo
  r/DCRfiles/Energy/bungee4s.dcr

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• Out of chaos, comes order.
• The scientific explanation notwithstanding , this
  is some neat  stuff to watch 
•        Harvard  built a device with a series of
  fifteen pendulums in a row,  each one of them
  slightly longer than its neighbor.     The
   pendulums were set into motion and the result
  was captured on  video.  The  patterns that
  appear in this short video are fascinating to
   watch and to think about.  Prepare  to be
  captivated by this simple device !Click on the
   below link but before starting the video, READ
  the complete  explanation.  Fascinating.   I
   want one !http//sciencedemonstrations.fas.harv
  ard.edu/icb/icb.do?keywordk16940pageidicb.page8
  0863pageContentIdicb.pagecontent341734statemax
  imizeviewview.doviewParam_nameindepth.htmla_i
  cb_pagecontent341734

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Refer to your definitions and answer

1. The ____________________ is the time of one
   complete vibration.
2. The ____________________ of vibratory motion is
   the number of vibrations per second.
3. The frequency is the ____________________ of the
   period.

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• An object suspended so that it can swing back and
  forth about an axis is called a
  ___________________.
• An ideal is one where all mass is considered to
  be concentrated in the __________.
• A pendulum exhibits SHM.

pendulum
bob
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The Pendulum Formula

• T period (s)
• l length (m)
• g acceleration due to gravity (m/s2)

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Refer to the pendulum formula and answer the
following statements

• How does mass affect period?
• What is the relationship between length and
  period?
• What is the relationship between acceleration of
  gravity and period?

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Refer to the pendulum formula and answer the
following statements

• How does mass affect period?
• It doesnt!
• What is the relationship between length and
  period?
• period is directly proportional to the square
  root of its length
• What is the relationship between acceleration of
  gravity and period?
• period is indirectly proportional to the square
  root of the acceleration of gravity

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Example 4

• What is the period of a pendulum that
• is 0.35 m long at sea level?

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Example 5

• The frequency of a moving pendulum
• measures 23 oscillations per 4.3 secs. Determine
• the length of the pendulum.
• First determine period
• 0.187 sec
• Rearrange pendulum formula to solve for length
• l 0.00868 m

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Example 6

• How do the periods of two pendulums compare if
  one has a measure of 25 cm and the other has a
  measure of 100 cm?

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Example 6

• How do the periods of two pendulums compare if
  one has a measure of 25 cm and the other has a
  measure of 100 cm?
• .25 m T 1sec
• 1.0 m T 2sec

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Refer to the formula for calculation of period

• If one knew the length and period, what could one
  calculate?
• GRAVITY!!!!

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REVIEW What does period of a pendulum depend
on?

• The period of the pendulum is directly
  proportional to the square root of the length and
  inversely proportional to the square root of the
  acceleration due to gravity.
• The longer the pendulum, the greater the period.

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Refer to the formula for calculation of period

• If one knew the length and period, what could one
  calculate?
• GRAVITY!!!!

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pendulum wave applet vibrating spring wave applet

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WAVES

• Demo

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What is a wave (continuous wave)?

• A repeating and periodic disturbance that
  transfers energy from one place to another
• They are an energy transport system
• WAVES TRANSPORT ENERGY NOT MATTER!!!
• The particles in a wave vibrate however they do
  NOT move along with the wave, only the wave front
  itself moves on.

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What is a pulse?

• A pulse is a single non repeated disturbance

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Types of Waves
Waves are classified by 1) The use of a medium
or not to carry the energy 2) The way they
vibrate relative to the motion of the wave
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Medium required to transfer energy

• Referred to as Mechanical Waves
• can be transmitted through solids, liquids, and
  gases.
• they can not travel through space
• Examples include sound waves and water waves.

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Medium NOT required to transfer energy

• Referred to as Electromagnetic Waves (Non
  Mechanical)
• are able to transmit energy through a vacuum as
  well as solids, liquids, and gases.
• They can travel through space NO medium required

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• Examples of electromagnetic waves include
• cosmic, gamma, x-ray, ultraviolet, visible light,
  infrared, microwave, radio
• All waves on the EM Spectrum

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ELECTROMAGNETIC WAVES

• All e/m waves travel through free space at a
  speed of approximately
• 3.00 x 108 m/s or 186,000 miles/sec.
• This speed is known as the speed of light c.

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Categorize on direction of particle movement

• Longitudinal
• Transverse

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Types of Wave Motion Longitudinal and Transverse
WaveMotion
Transverse
Compressional (Longitudinal)
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Transverse Wave Motion
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• Transverse Waves

Motion of Molecules
Direction of Wave
Vibration is perpendicular (up down) to the
direction the wave is moving. ex.
light waves, snakey
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Transverse Wave Diagrams
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Longitudinal (Compressional) Waves
vibration is parallel to the direction of the
wave. These waves require a medium (such as
air or water) through which to travel. ex.
Sound waves (looks like a spring)
Direction of Movement
Direction of Wave
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Longitudinal Wave Motion
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Contd
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Longitudinal Waves Anatomy

• Rarefaction region in which the particles are
  spread out
• Compression region in which the particles are
  close together
• A wavelength composed of a complete rarefaction
  and a complete compression.

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Common Wave Properties

• Frequency and period are inversely related. T1/f

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Calculating Wave Speed v f?

• Where
• v wave speed in m/s
• f frequency in Hz
• ? the wavelength in meters.

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Which wave has the longest wavelength?
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Which wave has the greatest frequency?
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What is the relationship between f and ? when
velocity held constant?

• inversely related

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IMPORTANT

• The speed of the wave however depends solely on
  the medium through which a wave is traveling

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Velocity of a Wave

• The equation vd/t can also be applied.

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fyi

• The frequency of the wave is determined by the
  motion of the vibration of the source and the
  speed of a wave changes when it moves from one
  medium to another, therefore, the wavelength must
  change in response when the wave moves into a
  different medium.

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Ex 7

• A tuning fork with a frequency of 583 Hz is
  vibrated, generating a sound wave. Measurements
  indicate that the wavelength of the sound wave
  being generated by the tuning fork is 0.59 m
  long. Calculate the speed of sound in air using
  this information.

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Ex 8

• A water wave travels 94.6m in 0.285 seconds.
  What is the velocity of the wave?
• Use v d/t
• 332 m/s

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How can you tell

• How much energy a wave is going to have?

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Energy and Amplitude

• The rate at which energy is transferred by a wave
  depends on the _________ of the wave.
• Energy of a wave IS NOT related to the speed of
  the wave.

amplitude
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Which wave has greatest amplitude?
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What is wrong here?
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Example Measurements show that the wavelength of
a sound wave in a certain material is 18.0 cm.
The frequency of the wave is 1900 Hz. What is the
speed of the sound wave?
? 0.18 m f 1900 Hz
v ? f 0.18 (1900) 342 m/s
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Wave Behavior at Boundaries

• Reflection
• Refraction
• Diffraction
• Interference

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Waves at Boundaries

• Remember speed of a wave depends on
• the medium the wave is passing through
• not the energy that created the vibrations.
  Energy only determines amplitude

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What is this?
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Reflection

• Reflection is the bouncing back of a wave at a
  boundary.

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Law of Reflection
the angle of incidence is equal to the angle of
reflection
Sound can also be reflected
Reflected sounds are Echoes
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Does reflection just apply to lights and mirrors?
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Reflection

• A reflected sound wave is called an echo.
• The wave equation v f? as well as the equation
  v d/t can both be used for sound waves.

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Reflection from a Free end (Dense to less Dense
Boundary)
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Reflection from a Closed end (less Dense to more
Dense)
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What the heck????
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You tube Amazing Water Trick

• http//www.youtube.com/watch?v8T8G_4H_TNg

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What is Refraction?
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Refraction

• Refraction is the change in direction of a wave
  at a boundary as it passes from one medium to
  another due to the change in wave speed.
• The speed changes however the frequency stays the
  same.
• This means that the wavelength must change.

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For refraction to occur,
the wave must change speed
and must enter the new medium at an oblique angle.
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Refraction occurs because wave speed changes in
different materials
In medium 2, the wave travels slower than in
medium 1. This change in speed causes a bending
toward the normal of the wave. This behavior is
important in lenses
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Diffraction
the spreading of a wave around a barrier
or through an opening
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In order for diffraction to occur, the opening or
edge must be much smaller than the incident wave
These images are created by a ripple tank
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Diffraction
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Diffreaction Applications

• Holograms (Not just depth, in it)
• Investigation of Molecular Structure

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Double Slit Diffraction

• Results in constructive and destructive
  interference

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adding waves
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Interference

• the result of the superposition of two or more
  waves, i.e. two or more waves occupy the same
  place at the same time.

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constructive vs. destructive interference

• Interference can be either constructive (build)
  or destructive (cancel).
• Depends on how the waves overlap

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Constructive interference

• waves align in sync or in phase
• displacement is in same direction
• Resultant wave has greater amplitude than
  orignal waves
• .

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Destructive interference

• waves are out of sync(out of phase)
• displacement is in opposite direction
• Resultant wave has smaller amplitude than orignal
  waves
• Total destruction if waves of equal amplitudes
  meet 180O out of phase

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Types of Interference
Constructive results in a larger amplitude
Destructive results in a smaller amplitude
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constructive vs. destructive interference

• According to superposition, the displacement of
  the medium caused by two or more waves is the
  algebraic sum of the displacements caused by the
  individual waves.
• If an wave with an amplitude of 8cm has
  constructive interference with a wave with an
  amplitude of 6cm, the resulting amplitude is
• 14cm

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Interference
Examples
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Superposition Principle
the displacement of the medium when two or more
waves pass through it at the same time is the
algebraic sum of the displacements caused by the
individual waves
These two wave pulses are moving towards each
other. What will happen when they are on top of
each other?

• Notice that wave A has an amplitude of 2, while
  wave B has an amplitude of 1.
• Both of the wave pulses are erect, so we say that
  they have positive values
• As they come together in the middle, both of them
  are pulling upwards

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When they are directly over each other, they are
both shoving particles up together, so the two
waves become one big wave with an amplitude of 3
for an instant.
NOTE They are still two separate waves, they
just happen to be in the same spot at the same
time.
They will continue moving on and look exactly the
way they looked before they hit each other.

• This is an example of Constructive Interference.

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These two wave pulses are going to collide. What
will happen?

• Notice that A and B are still the same amplitude,
  but now B is inverted.

For a moment the two wave pulses become one
smaller wave pulse with an amplitude of (2 -1
1) positive one. This is Destructive
Interference
And after they pass
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node vs antinode

• node a point in a medium that is completely
  undisturbed when a wave passes.
• Antinode the point of maximum displacement it
  can be either a crest or a trough

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Standing Wave A result of interference

• Created when two periodic waves of equal
  amplitude and wavelength travel in the opposite
  direction.
• the nodes and antinodes of a wave are in a
  constant position.
• as the frequency of the wave increases, the
  number of nodes and antinodes increases in the
  same amount of space.

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