Waves

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• Waves Sound

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Waves
1a. A wave is a rhythmic disturbance that
transfers energy. b. All waves are made by
something that vibrates. Energy is REQUIRED!!
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2. Mechanical waves need a matter medium to
travel through. (sound, water, seismic) 3. Two
basic types of waves a. Transverse
b. Compressional (longitudinal)
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4. Wave properties a. Wavelength -
distance from a point on a wave to the same
corresponding point on the next wave. b.
Frequency - number of waves that pass a point in
one second (expressed in Hz).
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c. Wavelength has an inverse relationship
to wave frequency. d. Wave velocity depends
on the type of wave and medium. 1)
Sound is faster in more dense media and in higher
temps. 2) Light is slower in more
dense media, but faster in a vacuum.
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3)
e. Amplitude - size related to the energy
carried by the wave. 1) Transverse -
how high above or how low below the middle line.
2) Compressional - how dense the medium
is at the compressions rarefactions.
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HARMONIC MOTION

• Motion that is repetitive.
• Examples include????????
• Linear motion would be motion that is simply in
  one direction.

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Simple Harmonic Motion

• Take a pendulum

• Period (T) seconds
• The time to complete one cycle
• Frequency (f) 1/sec Hertz Hz OR cycles/sec
• Number of cycles per unit time

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Pendulum Periodic motion

• Frequency 1/ period
• Period 1/Frequency

• Period is the time for an object to oscillate
  back and forth
• Usually used in a pendulum and depends on the
  length of the string and gravity.

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Simple Harmonic Motion
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Simple Harmonic Motion

• Take an object in circular motion
• At a constant angular speed, ?
• Each revolution
• Angle of 2p radians

• Since the of cycles it makes per second is
  frequency, f
• The of radians it moves per second

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Simple Harmonic Motion

• Since the of cycles it makes per second is
  frequency, f
• The of radians it moves per second

• Angular frequency - ?

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Simple Harmonic Motion
Imagine the dot below is a projection of the dot
on the circle on a horizontal axis
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Simple Harmonic Motion
Imagine the dot below is a projection of the dot
on the circle on a horizontal axis
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Simple Harmonic Motion
Same motion this time the below dot is black
and on the horizontal axis of the circle with the
origin at the center.
The black dot is in simple harmonic motion with
the same period and frequency as the rotating
circle
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Amplitude

• When using a pendulum the size that it moves from
  the midline or how big the cycle is.

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Damping

• The gradual loss in amplitude of a swinging
  pendulum. Friction and gravity are the main
  causes of damping.

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Hookes Law

• Hooke's Law states that in an elastic
  material strain is proportional to stress.  The
  point at which a material ceases to obey Hooke's
  Law is known as its elastic limit.

• F -k x
• PEsp ½ k x2

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• Hooke's law is the relationship between the force
  exerted on the mass and its position x. Consider
  a object with mass m, that is on a frictionless
  surface and is attached to a spring with spring
  constant k. The force the spring exerts on the
  mass depends on how much the spring is stretched
  or compressed, and so this force is a function of
  the mass's position.

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The spring constant is increased by a factor of 2
from left to right.
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5. Wave behavior a. Reflection - the
bouncing back of a wave. 1) Sound echoes
2) Light images in mirrors 3)
Law of reflection i r
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Refraction..

• The bending of waves.
• Caused by a change in speed
• Greater the difference in speed, more the light
  is bent
• Direction of bending depends on speed of light in
  both materials
• If speed slows, light is bent toward the normal
• If speed increases, light is bent away from the
  normal
• Amount of refraction depends on wavelength
• Shorter wavelength, more it bends

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b. Refraction - the bending of a wave
caused by a change in speed as the wave moves
from one medium to another.
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The girl sees the boys foot closer to the
surface than it actually is.
If the boy looks down at his feet, will they seem
closer to him than they really are?
No! He is looking straight down and not at an
angle. There is no refraction for him.
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3) Diffraction depends on the size of
the obstacle or opening compared to the
wavelength of the wave.
Less occurs if wavelength is smaller than the
object.
More occurs if wavelength is larger than the
object.
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c. Diffraction - the bending of a wave
around the edge of an object.
1) Water waves bending around islands
2) Water waves passing through a slit
and spreading out
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4) AM radio waves are longer and can
diffract around large buildings and mountains FM
cant.
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d. Interference - two or more waves
overlapping to form a new wave.
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1) Constructive (in phase) Sound waves
that constructively interfere are louder
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2) Destructive (out of phase) Sound
waves that destructively interfere are not as loud
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Which is which???
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e. Standing wave - a wave pattern that
occurs when two waves equal in wavelength and
frequency meet from opposite directions and
continuously interfere with each other.
node
antinode
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Resonance on strings

• Secured at both ends and has a node at each end.

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Nodes and Antinodes

• As a standing wave waves back and forth (from the
  red to the blue position), there are some spots
  called nodes that do not move at all basically
  there is no change, no waving up-and-down (or
  back-and-forth), at these spots. The spots at the
  biggest part of the wave - where there is the
  most change during each wave - are called
  antinodes.

• Nodes and Antinodes

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• http//www.musemath.com/flash/long_wave1.html
• http//www.musemath.com/flash/modesofvibration2.ht
  ml

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• There is a whole set of standing waves, called
  harmonics, that will fit into any "container" of
  a specific length. This set of waves is called a
  harmonic series. Standing Wave Harmonics

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• http//id.mind.net/zona/mstm/physics/waves/standi
  ngWaves/standingWaves1/StandingWaves1.html

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Nodes and antinodes

• Frequency ( antinodes)(wave speed)
• 2(length)

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• The lowest frequency resonance (the
  "fundamental") occurs when all atoms are moving
  together in a synchronized fashion. The next
  highest frequency (the "first overtone") occurs
  when half of the atoms on one side of the body
  are moving opposite to the half on the other
  side.

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• http//www.musemath.com/flash/modesofvibration2.ht
  ml

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• When the string player puts a finger down tightly
  on the string,
• How has the part of the string that vibrates
  changed?
• How does this change the sound waves that the
  string makes?
• How does this change the sound that is heard?

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When a finger holds the string down tightly, the
finger becomes the new end of the vibrating part
of the string. The vibrating part of the string
is shorter, and the whole set of sound waves it
makes is shorter.

• The part of the string that can vibrate is
  shorter. The finger becomes the new "end" of the
  string.
• The new sound wave is shorter, so its frequency
  is higher.
• It sounds higher it has a higher pitch.

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• Calculation of ?

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f. Resonance - the ability of an object to
vibrate by absorbing energy at its natural
frequency.
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http//www.archive.org/details/SF121

• Resonance is the place were thing like to move or
  vibrate.

• http//www.youtube.com/watch?vP0Fi1VcbpAI
• http//en.wikipedia.org/wiki/Tacoma_Narrows_Bridge
  
• http//encarta.msn.com/media_461550807/collapse_of
  _the_tacoma_narrows_bridge.html

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How does sound relate to resonance?
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Sound- compressional wave 1. Energy is
transferred from particle to particle through
matter. 2. How we hear a. Outer ear
collects sound. b. Middle ear amplifies
sound. c. Inner ear converts sound.
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3. Properties of sound a. Intensity and
loudness 1) Intensity depends on the
energy in a sound wave. 2) Loudness is
human perception of intensity. 3)
Loudness is measured on the decibel scale.
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a) Threshold of hearing (0 db)
b) Threshold of pain (120 db)
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b. Frequency and pitch 1) High
frequency means more vibrations hitting the ear.
2) Pitch is how high or how low a sound
seems to be. 3) Healthy humans can
hear from 20 Hz to 20,000 Hz 4) We are
most sensitive from 440 Hz to 7,000 Hz.
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5) Ultrasonic sound has a frequency
greater than 20,000 Hz. a) Dogs (up
to 35,000 Hz) b) Bats (over 100,000
Hz) c) Medical diagnosis 6)
Infrasonic sound has a frequency below 20 Hz
they are felt rather than heard (earthquakes,
heavy machinery).
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c. Speed of sound 1) 332 m/s in
air at 0 C. 2) Changes by 0.6 m/s for
every Celsius degree from 0 C. 3)
Subsonic slower 4) Supersonic
faster than sound (Mach 1 speed of sound)
5) Sonic boom (pressure cone)
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d. The Doppler effect the change in pitch
due to a moving wave source. 1)
Objects moving toward you cause a higher pitched
sound. 2) Objects moving away cause
sound of lower pitch. 3) Used in radar
by police and meteorologists and in astronomy.
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Blue shift vs. red shift.

• Blue shift vs. red shift.

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4. Musical sound a. Noise has no pattern.
b. Music has a pattern and deliberate
pitches. c. Sound quality describes
differences of sounds that have the same pitch
and loudness. d. Every instrument has its
own set of overtones.
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e) Beats are pulsing variations of
loudness caused by interference of sounds of
slightly different frequencies.
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Beats

• When two sound waves of different frequency
  approach your ear, the alternating constructive
  and destructive interference causes the sound to
  be alternatively soft and loud - a phenomenon
  which is called "beating" or producing beats. The
  beat frequency is equal to the absolute value of
  the difference in frequency of the two waves.

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• When two notes are played at the same time and
  are of very similar frequencies, the sound
  resulting is often heard as a regular fluctuation
  - a beat.

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• .
• The sound produced will have an average frequency
  of (f1f2)/2 but will "beat" with a different
  frequency. In the regions of constructive
  interference the sound will be at a maximum
  level in regions of destructive interference it
  will be at a minimum. Hence the sound will waver
  in volume or beat.
•  ( f1f2)/2

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PIPES

• The lowest perceived frequency is called the
  fundamental.
• A closed pipe will resonate at odd number
  multiple frequencies.
• F1 v/ 4L
• Open pipe instruments have a fundamental
  frequency at the 1st harmonic f v/2L

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Longitudinal Waves in Pipes
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• Pipe open at both ends (column of air)
• Examples flute and many wind instruments,
  culvert, etc.
• Each end is an antinode.
• Number of nodes n
• Number of antinodes n 1
• n 1, 2, 3, 4 . . .
• Pipe open at one end, closed at other end
• Examples reed instrument, certain organ pipes,
  straw in a drink, etc.
• Open end is an antinode.
• Closed end is a node.
• Number of antinodes Number of nodes
• n 1, 3, 5, 7 . . . (only odd harmonics
  occur!)

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Open pipes

• An open pipe resonator is resonating with both
  ends open that also will resonate with a sound
  source.
• The sound wave reflects off the OPEN end
  therefore making the pressure inverted.

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Fig 11.45, p.403
Slide 74
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Closed Pipe

• The shortest column of air that can have an
  antinode at the closed end and a node at the open
  end is ¼ of a ?.
• As frequency is increased resonance is found at ½
  ? intervals

• F nv / 4L

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Fig 11.44, p.403
Slide 76
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5. Uses of sound a. Acoustics the study
of sound.
Soft materials dampen sound hard materials
reflect it (echoes and reverberations).
b. SONAR Sound Navigation and Ranging
(echolocation). c. Ultrasound imaging d.
Kidney stones gallstones.
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• http//physics.bu.edu/duffy/classroom.html

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Hooks law lab

• http//phoenix.phys.clemson.edu/labs/124/shm/index
  .html

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B. Pitch how high or low a note is due
to frequency 1. ultrasonic above
audible range 2. infrasonic below audible
range EX/ human range 20-20,000
Hz animal range 20-25,000
Hz porpoise, bats 20-150,000 Hz
IV. How does sound behave?
A. Resonance when two objects vibrate
with the same frequency EX/ Tacoma Narrows
Bridge
B. Interference overlapping of 2 sound
waves 1. constructive increases
amplitude 2. destructive -- decreases
amplitude difficult to achieve
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Nature of Sound in Air

• Sound requires a medium.
• solid, liquid or gas
• Demo Bell in a evacuated Bell Jar
• Sound Box
• Sound waves have compression and rarefaction
  regions.

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Speed of Sound in Air

• 340 meters/second
• 760 miles/hour
• Mach 1
• Chuck Yaeger.X-1

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SPEED OF SOUND
How it varies
increases with humidity increases with
temperature increases with density
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• V 331 (l T/273) .5

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Resonance

• The place where a wave like to vibrate.

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Determines resonance

• Tension and mass of string will cause the speed
  to vary.
• tension will cause a faster wave and higher
  frequency.

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GOIN Sharp or Flat???

• temp causes speed of sound.
• In a woodwind instrument there is little change
  in in the length, which determines the ? with a
  change in temp. so there is only a slight
  increase in pitch. (sharp)
• A string expands with increased temp thus causing
  tension and a in frequency.

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Fig 11.46, p.404
Slide 92
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• Hooke's Law states that in an elastic
  material strain is proportional to stress.  The
  point at which a material ceases to obey Hooke's
  Law is known as its elastic limit. 
• The first part is very easy. It means that the
  bigger the weight (stress) you hang on the string
  the more it will stretch (strain). 
• The second part is also easy. Whilst the elastic
  limit is not exceeded, the string will go back to
  its original length when you take the weights off
  it, but if you add too much weight, the string
  will stretch without going back to its original
  length when you take the weights off it. If you
  leave a very large weight hanging on the string,
  it will gradually get longer and longer until it
  breaks. In this state the wire is behaving as if
  it were a fluid instead of a solid.

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•    
• The general law of mechanics that stress is
  directly proportional to strain
• where is a constant of proportionality known as
  the shear modulus. Plugging in the definitions
  for shear stress and strain,

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Waves computer

• http//www.sciencejoywagon.com/physicszone/09waves
  /