Waves and Sound

1
Waves and Sound

• Chapter 11

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Ways to Transport
                                               
                                                  
                                                  
                    Image right Recent Cassini
images of Saturn's moon Enceladus backlit by the
sun show the fountain-like sources of the fine
spray of material that towers over the south
polar region. Image credit NASA/JPL/Space
Science Institute Full image and caption
Movie Enceladus plumes Browse version of image

• Two ways to transport energy and momentum
• Streaming particles
• Flowing waves

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Sound

• Two ways to study
• Psychological (mind) and physiological (body)
• What we hear
• Physical
• What sound is compression wave

4
Waves

• Moving self-sustained disturbance of a medium
• Medium
• Field
• Substance
• Mechanical wave in material media

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Wave Characteristics

• Atoms
• Push together repel
• Pull apart attract
• Objects are made of atoms
• When atoms are distorted they act like attached
  by springs
• Displacement causes a wave

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Progressive or Traveling wave

• Self-sustaining disturbance
• Examples
• String
• Liquid waves
• Sound waves
• Compression waves
• The main difference between particle stream and
  wave is
• Medium stays in place as the wave progresses

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Wave Forms

• Longitudinal
• Sustaining medium is displaced parallel to the
  direction of propagation
• Ex Sound waves
• Transverse
• When the sustaining medium is displaced
  perpendicular to the direction of propagation
• Ex Guitar string
• Torsion
• Variation of transverse waves
• Water waves
• Combination of Longitudinal and Transverse waves

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Types of Waves

• Longitudinal move
• back and forth
• Transverse move
• up and down
• Water move in circle

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WavePulse

• One cycle of a wave
• Profile outline or shape of the wavepulse
• Determined by the driver of the wave
• Speed Determined by the medium
• Examples
• Gunshot
• Grunt
• Tsunami

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WaveTrain

• Disturbance of waves with a beginning and end
• Amplitude varies
• Carrier wavelength Steady sinusoidal oscillation

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Periodic

• Ideal disturbance composed of endless repeats of
  the same profile wave

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Labeling a Wave

• Period how long it takes one profile to pass a
  point in space
• Frequency number of profile waves passing per
  second
• Wavelength ? (lambda) - distance in space over
  which the wavetrain executes one cycle
• Amplitude Height of the waves

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Velocity of Wave

• v f?
• V velocity (m/s)
• f frequency (cycles/sec or Hz)
• ? wavelength (m)

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Problem

• Waves pass the length of a 4.5 m boat. It takes
  1.5 seconds for the wave to go from end to end.
  If the waves are 0.5 seconds apart, what is the
  period, frequency and wavelength?
• T 0.5 seconds
• f 1/T 1/0.5 2.0 Hz
• v L/t 4.5 m/1.5 sec 3.0 m/s
• ? v/f 3.0 m/s / 2.0 Hz 1.5 m

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Transverse Waves Strings

• Speed of the waves is determined by the
  properties of the medium, not in any way the
  motion of the source
• Velocity of wave in string
• v vFT/m/L
• v - velocity (m/s)
• FT Tension (N)
• m /L mass/unit length

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Problem

• What is the speed of a wave pulse in a 20 cm, 40
  g guitar string with the tension of 19.6 N?
• v vFT/m/L
• v - ?
• FT 19.6 N
• m /L .040 kg / 0.20 m 0.020 kg/m
• v vFT/m/L
• v19.6 N / 0.020 kg/m
• 31 m/s

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Reflection, Absorption, Transmission

• Reflected carries all the original energy
• Absorbed Friction stops wave
• Transmission moving from one media to another
• Velocity may change when moving between medias

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Compression Waves

• Solids longitudinal elastic wave
• Ex Earth quake
• Fluids acoustic waves
• Ex sound waves
• Parts
• Rarefaction distance between atoms is elongated
• Compression distance between atoms is squeezed
• Direction of movement in the direction of
  oscillation
• Each atom is in SHM

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Speed of Waves in Media

• Can be determined by the restoring force and its
  density
• Use
• Bulk Modulus
• Bernoullis equation
• Youngs Modulus

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Ultrasound

• Dolphins use chirps to locate items underwater
• Size of wave 1.4 cm
• Can see fish and other small items
• Above our hearing range - 105 Hz

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Other uses of Ultrasound

• Autofocus cameras
• Bats
• Medicine
• Tumor and Kidney stone destruction
• Probe body
• Joints
• Baby

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Infrasound

• Wave lengths below our hearing range (less than
  20 Hz)
• Examples
• Elephants
• Submarines
• Subwoofers in Rock Bands
• Vibrate our internal organs
• http//www.pbs.org/wnet/nature/animalspredict/vide
  o2.html

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SOUND

• Human hearing range 20 Hz to 20 khz
• Usually can not hear through entire range
• Diminishes with age (above 20 years) and loud
  noises

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Acoustics

• First considered in Rome
• Marco Vitruvius Pollio designed amphitheaters
• Though sound travel through air like water waves
• Sound needs a media to travel through
• No sound in a vacuum
• No sound in
• explosions in space

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Making Waves

• Speaker vibrates
• Creates pressure variations
• Quiet less than 0.002 Pa
• Loud about 10 Pa
• Loudness depends on how far the air molecules
  move
• Period and Frequency depends on time for
  speaker to move through a cycle
• Wavelength distance
• between rarefactions

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Problem

• What is the wavelength of a tuning note (A440)
  which is 440 Hz. The speed of sound at room
  temperature is 343.9 m/s?
• ? v/f 343.9 m/s / 440 Hz 0.782 m

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Superposition of Waves

• Waves can move through the same area of space and
  have a combined effect
• Are not changed or scattered
• Superposition Principle -When two waves overlap,
  the resultant is the algebraic sum of various
  contributions at each point

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Fourier Analysis

• Jean Baptiste Joseph, Baron de Fourier
• Proved that a periodic wave having a wavelength
  can be synthesized by a sum of harmonic waves
• A wave profile is a result of overlapping sines
  and cosines

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Wavefront and Intensity

• Waves move out in a circle or sphere
• In-phase at different distances
• As the wave moves out it becomes diffused

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Acoustic Power

• Power Joules/sec Watts
• P Work/sec
• Joules Newton-meters
• Work Force x Distance
• Measuring
• Depends on area the detector
• Depends on the amount of time

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Intensity

• The average power divided by the perpendicular
  area across which it is transported
• I Pav/A (Watt/meter²)
• Area of spherical wave 4?R²
• The farther from the source, the greater the
  area, therefore the less the intensity

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Inverse Square Law

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Problem

• An underwater explosion is detected 100 m away,
  where the intensity is 1.00 GW/m². About 1 second
  later the sound wave is recorded 1.5 km away from
  the explosion. What will its intensity be?
• R1 100 m R2 1.5 km
• I1 1.00 GW/m² ?t 1 sec
• Power in first square power in second square
• I1 4?R² I2 4?R²
• I2 (1 x 10? W/m²) (100 m)² / (1500 m)² 4.4 x
  106 W/m²

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Speed of Sound in Air

• In 1636, Father Mersen used echoes to measure
  speed of sound
• Speed of sound increases with temperature of air
• Air temperatures arent constant
• Velocity varies depending on the gas
• Speed of sound does not depend on frequency
• All waves get there simultaneously

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Problem

• During a thunder storm, you hear thunder 3.50
  seconds after you see a bolt of lightening. How
  far away, in meters and miles, did the lightening
  strike?

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Hearing Sound

• Three parts of ear
• Outer From outer ear to ear drum
• Sound resonates in canal
• Amplifies waves from 3 kHz to 4 kHz
• Middle links eardrum to 3 bones to oval window
• Increases sound pressure
• Inner Transducer that converts pressure to
  electrical impulses
• Hairs in the cochlear vibrate at different
  frequencies and amplitude

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Pitch

• Human response to frequency
• Pure tone sine wave
• Higher the frequency, the higher the pitch
• Varies in people
• Increasing intensity makes you think you also
  increased pitch
• Human voices
• Men 80 Hz 240 Hz (700 Hz in song)
• Woman 140 Hz 500 Hz (1100 Hz in song)

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Timbre

• Waveform blend of
• Harmonic fundamental tone (f)
• Overtones tones that are over the harmonic
• May or may not be harmonics (2f, 3f, etc)
• Combination
• of harmonic
• and overtones
• makes the
• timbre

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Intensity - Level

• Intensity-level
• Number of factors of 10 that is its intensity is
  above the threshold of sound
• measured in bel (In honor of Alexander Graham
  Bell)
• Io(hearing) 1.0 x 10¹² W/m²
• Decibel (dB) 1/10th of a bel
• Unitless
• ß 10 log10 I / Io
• Condenses the range from 1.0 to a million
  millionth to 0dB to 120 dB

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Logarithm identities

• Log A/B log A log B
• Log AB log A log B
• ß 10 log I / Io
• ?ß 10 log I1 / I2
• This means that if you have a 12-W system and
  want to make it 2X louder, you have to increase
  the power to 120-W

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Noise

• Noise Unrelated jumble of disturbances
• Non-periodic
• Continuous frequency
• White noise broad bandwidth of sounds out equal
  intensities
• Ex wind, pouring water, radio static
• We can distinguish between wavepulses up to about
  20 beats per second then it becomes a hum

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Beats

• Interference caused in sound waves of different
  frequency
• Used to tune guitars and pianos
• Carrier wave f1 f2 / 2
• Beat frequency f1 - f2
• f1 higher f

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Standing Waves

• Waves reflected back and forth in a finite medium
• Very common
• All instruments
• Our speaking and
• singing voice
• Ringing bells
• Lasers

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Nodes and Antinodes

• Nodes when the resultant is zero
• Antinodes midway between nodes
• Wavelength twice the node-to-nodes distance

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Standing Waves on Strings

• First harmonic
• Fundamental
• 2nd harmonic
• 1st overtone
• 3rd harmonic
• 2nd overtone
• 4th harmonic
• 3rd overtone
• 5th harmonic
• 4th overtone

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String Standing Wave systems

• Resonance in the system
• Amplifies the input
• Guitar
• Each string has a different tension and linear
  mass-density
• Fingering Changes the length of the string
  increases the fundamental frequency
• L ½ N? (N - whole number of nodes)
• fN N/2L FT/m/L
• Falsetto voice increase tension to increase
  frequency

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Problem

• What must the tension on a 300 mm fiddle string
  be to be tuned to 660 Hz? The mass-length is
  0.38 g/m.
• FT (m/L)(2Lf)²
• 0.38 g/m (2 x 0.300 m x 660 Hz)²
• 72 N (about 16 lbs)

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Strings and Amplification

• Strings are not loud
• Sounding board (piano)
• Sounding box (guitar and violin)
• Pick-ups in electric guitars

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Standing Waves in Air Columns

• Made in air-filled chambers (wind pipe, trumpets,
  organ pipes)
• Made by vibrating reeds (saxophone), lips on
  mouth pieces(trumpet) , fluttering jet of air
  (flute)
• Only frequencies that fit the standing wave mode
  will be sustained and amplified

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Types of columns
Types of columns

• Open on both ends
• Closed on both ends
• Open on one end and closed on the other

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One open end

• L ¼ N?
• fN Nv/4L (v speed of sound)

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Double open pipe

• L ½ N?
• fN Nv/2L (v speed of sound)
• Blowing slow fundamental
• Blowing fast harmonics

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Doppler Effect

• Frequency of pitch changes from high to low
• Eeeeeoooooo
• Think of bug in water swimming forward

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Doppler Effect Formulas

• fo fsv vo v vs
• The amount of frequency shift depends on who is
  moving
• Uses radar guns, weather tracking devices,
  satellites, blood flow
• Doppler effect when bounced off an approaching
  target and returned
• fo (v vt) fs/ v - vt

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Doppler Radar
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Doppler Effect and the Universe

• Red-shift of light galaxies are moving away
  from us
• Based on recession rates and apparent size of
  universe the Big Bang happened 15 thousand
  million years ago