Physics of Sound

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Physics of Sound
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Logarithms

• Do you know how to use your calculator?
• Find the following functions
• , - , x , / , , log
• The log is the exponent to which 10 is raised,
  representing a number

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Antilogarithm

• The antilog is 10 raised to the x power, or 10x

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Logarithms

• Solve the following together
• Log (20) ___________
• Log (400) ____________
• Solve on your own
• Log (0.5) ____________
• Log 2 _____________

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Antilogarithms

• Solve the following together
• X 2 _______________
• X 4.3 _______________
• Solve on your own
• X 8.5 _____________
• X 9.0 _____________

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What is sound?

• Any change in air pressure
• The molecules in the air exerts a pressure of
  over 1 ton per square foot on our ears
• Must be a rapid change in sound pressure to be
  heard, a small rapid change will create noise
• Travels as sound waves

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Frequency of Sound

• Rate at which complete high and low pressure
  regions are produced by the sound source.
• 1000 cycles per second is 1000 high and low
  pressure regions passing a point in one second.
  This is called 1000 Hertz (Hz) or 1 kHz.

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Speech frequencies

• Speech frequencies generally regarded to be 500
  to 3000 hertz
• Frequency range of perceivable sound 20 Hz to
  15,000 to 20,000 Hertz.
• Tuning forks

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Tone and Noise

• Tuning fork pure tone and related frequencies
• We cannot see the tines moving back and forth
  because they are moving back and for the too
  quickly. Two-hundred cycles a second is too fast
  to see.
• Noise random frequencies

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Noise travels through a medium

• A vibrating object creates a disturbance that
  travels through a medium
• A trains noise can travel through the steel
  tracks by creating sound waves
• The vibrations of a speaker creates sound waves
• Frequency is the number of complete back and
  forth vibrations per second

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Noise travel

• Vibrational motion of the medium is set up by the
  object.
• The vibrations set the molecule of the medium
  into motion.
• The motion of the molecule in the medium sets the
  molecule next to it, in motion.
• The transfer of energy continues as the vibration
  of one molecule sets the next molecule into
  motion.

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Sound wave is a pressure wave

• Thus an instrument can be used to measure the
  oscillations of high and low pressure variations
  in the pressure.
• These oscillations are shown as the typical sine
  wave that you may have seen

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Wavelength

• Distance which a disturbance travels along the
  medium in one complete wave cycle.
• Measured from one wave trough or crest to the
  next wave trough or crest, in a transverse wave.
  It is from one wave compression to the next wave
  compression in a longitudinal wave
• With a pressure wave it is from one high pressure
  region to the next high pressure region

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Speed of Sound

• Sound waves are pressure disturbances traveling
  through a medium by means of particle interaction
• How fast the disturbance is passed from particle
  to particle determines the speed of sound.
• How easily the medium transfers the disturbance
  determines the speed, which is measured in feet
  per second (ft/sec)

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Speed of Sound

• Speed is equal to distance traveled per unit
  time.
• Speed distance/time
• If a sound waves travels 2,300 feet in 2 seconds
  the sound is traveling at 1,150 ft/sec
• Examples of sound travel would be the time it
  takes for thunder to reach the observer and an
  echo

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Speed of Sound

• The speed depends on the properties of the
  medium, the elastic properties are much greater
  than are the inertial properties.
• Thus longitudinal sound waves will travel faster
  in solids than in liquids, and longitudinal sound
  waves will travel faster in liquids than in gases

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Speed of Sound in air

• The speed of sound in air will depend on
  temperature and pressure of the air. The
  relationship is
• C 1054 f/s (1.07 f/s/oF)xT

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Speed of Sound

• At 72 oF, the speed of sound is 1,130 f/s
• The delay between lightning and thunder.
• Light travels 980,000,000 f/s or reaches the
  observer in almost no time.
• The time delay of an echo is the same phenomenon,
  the distance of a reflecting surface can be
  determined by the time it takes for the echo to
  return

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Speed of Sound

• The speed of sound in different mediums at
  standard conditions
• In air the velocity is 1,130 f/s
• In water the velocity is 4,700 f/s
• In wood the velocity is 13,000 f/s
• In steel the velocity is 16,500 f/s

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Speed, frequency and wavelength

• The mathematical relationship between the three
  is
• C ? x f
• The speed is a constant based on the properties
  of the medium. The length of a wave will vary
  with the frequency.

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Speed, frequency and wavelength

• At standard conditions, the speed of sound is
  1,130 f/s. Say we have a 440 hertz frequency
  pure tone sound, what is the wavelength of the
  sound?
• C ? x f
• ? C / f
• ? 1,130 / 440
• ? 2.57 feet

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Speed, frequency and wavelength

• How about air at 1,000 oF as part of an exhaust
  stream?
• Find the speed of sound traveling through the
  exhaust?
• C 1,054 f/s (1.07 f/s)x oF
• C 1,054 1.071,000
• C 1,054 1070 2,124 f/s

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Speed, frequency and wavelength

• Engine rotating at 3,000 rpm and has 4 cylinders
• 3,000 4 12,000 rounds per minute
• Which equals 200 rounds per second (Hz)
• What is the frequency of this sound?
• ? C / f
• ? 2,124 / 200
• ? 10.62 ft

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Speed, frequency and wavelength

• What is the wavelength of the following
  frequencies? (at standard conditions)
• ? 20 hz ________ remember ? C/f
• ? 1000 hz ________
• ? 16000 hz ________

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Period

• The period is the time for one complete cycle of
  pressure transition. It is the reciprocal of the
  frequency.
• T (sec) 1/f
• The period of a 1000 Hz sound wave is
• T 1/f 1/1000 0.001 seconds

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Period

• What is the period of a 20 Hz and a 16,000 Hz
  wave?
• T20 Hz 1/f
• T16000 Hz 1/f

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Period

• Below 20 Hz infrasound
• Above 20,000 Hz ultrasound
• Dogs 50 Hz to 45,000 Hz
• Cats 45 Hz to 85,000 Hz
• Bats to 120,000 Hz
• Dolphins 200,000 Hz
• Elephant down to 5 Hz and up to 10,000 Hz

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Sound Waves

• A pure tone (tuning fork) sound introduced into
  the room will create a change in the molecules in
  the room.
• At 440 Hz the molecules will bunch up every 3
  feet
• Also there will be a net drift of molecules from
  the bunched up section to the section where the
  molecules are further apart.
• The wave is moving toward me at 1,130 f/s

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Sound Waves

• The sound wave is traveling toward me however,
  the molecules are not moving toward me.
• An example would be a garden hose, when I shake
  it a snaky wave travels away, however, the hose
  is not moving only the wave energy is moving
  along it.
• Other examples would include sound, water, and
  football fans

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Sound Waves

• Mechanical waves they require a medium to
  transfer energy. So sound will not transfer
  through a vacuum.
• Slinky demo
• Pulse and a wave moves one coil at a time
• Medium is the slinky. In water it is the water,
  at a concert it is the air, at a football game
  its the fans in the stadium

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Intensity

• The amount of energy which is transported past a
  given area of the medium per unit time
• Intensity energy / (time x area)
• Since power is energy per unit time, it can also
  be written as
• Intensity power / area
• Typical units are Watts/meter2

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Intensity

• Inverse square relationship
• The mathematical relationship of intensity and
  the distance from the source
• As you move away from the source (larger
  distance) the area gets larger and the intensity
  will decrease.
• If the distance from a source doubles the
  intensity will decrease by a factor of 4.

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Threshold of Hearing

• Humans can detect sound of very low intensity.
  The faintest sound which the ear can detect has
  an intensity of 1x10-12 W/m2.
• At this level sound will displace particles of
  air by a mere one-billionth of a centimeter.

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Loudness

• Loudness of a noise is a more subjective
  response. Factors that affect the perception of
  loudness includes age and frequency

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Sound Intensity

• The average rate at which sound energy is flowing
  through a unit area
• Intensity can be measured by means of a twin
  microphone probe, with signal processing by a
  microprocessor controlled cross correlation
  spectrum analyzer
• Measurement of intensity is very useful in
  industrial noise situations

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Decibels

• The decibel scale is a logarithmic scale. The
  logarithmic scale is based on multiples of 10.
• A sound which is 10 times more intense is
  assigned a sound level of 10 dB.
• A sound which is 100 times more intense is
  assigned a sound level of 20 dB.
• A sound which is 1000 times more intense is
  assigned a sound level of 30 dB.

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Decibels

• Threshold of hearing 0 dB
• Whisper 20 dB
• Normal conversation 60 dB
• Street traffic 70 dB
• Vacuum cleaner 80 dB
• Walkman at max setting 100 dB
• Threshold of Pain 130 dB
• Military Jet Takeoff 140 dB

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Sound Pressure and Sound Pressure Level

• Sound pressure is the root mean square (rms)
  value of the pressure changes above and below
  atmospheric when used to measure steady state
  noise.
• The sound pressure level is the ratio expressed
  in decibels (dB) of the rms pressure to a
  reference rms pressure.

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Sound Pressure Level

• Sound pressure level (Lp) is
• Lp 10 log (P / Po)2
• 20 log (P / Po)
• Where Po the reference sound pressure of 2 x
  10-5 N/m2
• Lp sound pressure level in dB
• P rms sound pressure in N/m2

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Sound Pressure Level

• For a sound source having a sound pressure of 1
  N/m2, what is the sound pressure level in dB?
• Lp 20 log (P/Po)
• 20 log ((1 N/m2)/(2x10-5 N/m2)
• 20 log (0.5 x 105) 94 dB

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Sound Pressure Level

• If the sound source has a sound pressure of
  2x10-3 N/m2, what is the sound pressure level in
  dB?

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Sound Pressure Level

• If the sound source has a sound pressure of
  2x10-3 N/m2, what is the sound pressure level in
  dB?
• Lp 20 log (P/Po)
• 20 log ((2x10-3 N/m2)/(2x10-5 N/m2)
• 20 log (1 x 102) 40 dB

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Sound Pressure Level

• Weighted sound levels Fletcher-Munson curves.
• Ear is most sensitive around 2 to 5 kHz

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Decibel Addition

• To add individual sound levels the equation to
  add these is
• LT 10log(10L1/1010L2/1010L3/10 10Ln/10)
• Example Two machines each operate at 93 dB at a
  given location. What is the sound pressure level
  if both machines are on?

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Decibel Addition

• Add to sound pressure levels of 93 dB together
• LT 10log(10L1/10 10L2/10)
• LT 10log(1093/10 1093/10)
• LT 10log(2 x 109.3) 96 dB

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Decibel Addition

• Exercise Three machines have the following
  sound pressure levels at a given measurement
  location 95, 96, 100 dB
• What is the resulting sound pressure level if all
  three machines are on?

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Decibel Addition

• Rule of thumb (can only be used when a limited
  number of sources are added together)
• 0 dB difference add 3 dB to the higher value
• 1-1.5 dB difference add 2.5 dB
• 2-3 dB difference add 2 dB
• 3.5 to 4.5 dB add 1.5 dB
• 5 to 7 dB add 1 dB
• 7.5 to 13 dB add 0.5 dB

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Decibel Addition

• Using the rule of thumb in the previous exercise,
  find the total sound pressure level

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Sound Pressure Level in decibels of common
sources of noise

• See page 38 and 39 in your manual
• Examples refrigerator 50 dB
• rainfall 50 dB
• doorbell 80 dB