Sound

1
Sound

• Chapter 15

2
Topics for Sound

• Sound wave properties
• Speed of sound
• Echoes
• Beats
• Doppler shift
• Resonance
• Anatomy of Ear

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Sound Wave Properties
4
Sound Waves are Longitudinal Waves
The air molecules shown below are either
compressed together, or spread apart. This
creates alternating high and low pressure.
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Frequency

• The frequency of a sound wave (or any wave) is
  the number of complete vibrations per second.
• The frequency of sound determines its pitch.

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The higher the frequency, the higher the pitch
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Wavelength

• Wavelength is the distance between two high
  pressures, or two low pressures. This property
  is dependent on the velocity of the sound and its
  frequency.
• Wavelength and frequency are inversely related.
• Short wavelength (high frequency) results in a
  high pitch.

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Frequency and the human ear

• A young person can hear pitches with frequencies
  from about 20 Hz to 20000 Hz. (most sensitive to
  frequencies between 1000 and 5000 Hz).
• As we grow older, our hearing range shrinks,
  especially at the high frequency end.
• By age 60, most people can hear nothing above
  8000 Hz.
• Sound waves with frequencies below 20 Hz are
  called infrasonic.
• Sound waves with frequencies above 20000 Hz are
  called ultrasonic.

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The Amplitude of a Sound Wave Determines its
loudness or softness
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Velocity of Sound
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The velocity of sound depends on

• the medium it travels through
• the temperature of the medium

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• Sound travels faster in liquids than in air (4
  times faster in water than in air)
• Sound travels faster in solids than in liquids
  (11 times faster in iron than in air)
• Sound does not travel through a vacuum (there is
  no air in a vacuum so sound has no medium to
  travel through)
• The speed depends on the elasticity and density
  of the medium.

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Effects of Temperature

• In air at room temperature, sound travels at
  343m/s (766 mph)
• v 331 m/s (0.6)T
• v velocity of sound in air
• T temperature of air in oC
• As temperature increases, the velocity of sound
  increases

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Relationship between velocity, frequency, and
wavelength

• V ?f
• V velocity of sound
• ? wavelength of sound
• f frequency of sound

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Echoes REFLECTION
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Echoes are the result of the reflection of sound
Sound waves leave a source, travel a distance,
and bounce back to the origin.
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Things that use echoes...

• Bats
• Dolphins/ Whales
• Submarines
• Ultra sound
• Sonar

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REFRACTION OF WAVES
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Refraction of Sound

• as the sound wave
• transmits into the
• warmer air at lower
• levels, they change
• direction, much like
• light passing through a prism

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DIFFRACTION

• THE BENDING OF WAVES THROUGH A SMALL OPENING

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BENDING OF A WAVE
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Sound waves move out like this

• http//www.kettering.edu/drussell/Demos/doppler/d
  oppler.html

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But when they move, the front of the wave gets
bunched up (smaller wavelength) and the back of
the wave starts to expand (larger wavelength)

• http//www.kettering.edu/drussell/Demos/doppler/d
  oppler.html

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Observer C hears a high pitch (high frequency)
Observer B hears the correct pitch (no change in
frequency)Observer A hears a low pitch (lower
frequency)

• http//www.kettering.edu/drussell/Demos/doppler/d
  oppler.html

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When the source goes faster, the wave fronts in
the front of the source start to bunch up closer
and closer together, until...
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The object actually starts to go faster than the
speed of sound. A sonic boom is then created.

• http//www.kettering.edu/drussell/Demos/doppler/d
  oppler.html

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Doppler Effect

• The doppler effect is a change in the apparent
  frequency due to the motion of the source of the
  receiver.
• Example As an ambulance with sirens approaches,
  the pitch seems higher. As the object moves by
  the pitch drops.

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Police use the Doppler Shift when measuring your
speed with radar

• A frequency is sent out of the radar gun
• The sound wave hits the speeding car
• The frequency is changed by the car moving away
  from the radar and bouncing back
• The amount the frequency changes determines how
  fast you are going
• The faster you are going, the more the frequency
  is changed.

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Equation that describes the doppler effect.

• f fo (v vo)
• (v - vs)
• fo is the actual frequency being emitted
• f is the perceived frequency as the source
  approaches or recedes
• vo is () if the observer moves toward the source
• vo is (-) if the observer moves away from the
  source
• vs is () if the source moves toward the observer
• vs is (-) if the source moves away from the
  observer

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Example

• Sitting at Six Flags one afternoon, Mark finds
  himself beneath the path of the airplanes leaving
  Hartsfield International Airport. What frequency
  will Mark hear as a jet, whose engines emit
  sounds at a frequency of 1000 Hz, flies toward
  him at a speed of 100 m/sec? (temp is 10oC)

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Solution

• v 331 (0.6)T
• v 331 (0.6)(10)
• v 337 m/s
• f fo(v vo) f ?
• (v vs) fo 1000 Hz
• vo 0 m/s
• vs 100 m/s

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Solution

• f 1000 (331 0)
• (331 100)
• f 1430 m/s

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Resonance
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Natural Frequency

• Nearly all objects when hit or disturbed will
  vibrate.
• Each object vibrates at a particular frequency or
  set of frequencies.
• This frequency is called the natural frequency.
• If the amplitude is large enough and if the
  natural frequency is within the range of 20-20000
  Hz, then the object will produce an audible sound.

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Timbre

• Timbre is the quality of the sound that is
  produced.
• If a single frequency is produced, the tone is
  pure (example a flute)
• If a set of frequencies is produced, but related
  mathematically by whole-number ratios, it
  produces a richer tone (example a tuba)
• If multiple frequencies are produced that are
  not related mathematically, the sound produced is
  described as noise (example a pencil)

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Factors Affecting Natural Frequency

• Properties of the medium
• Modification in the wavelength that is produced
  (length of string, column of air in instrument,
  etc.)
• Temperature of the air

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Resonance

• Resonance occurs when one object vibrates at the
  same natural frequency of a second object,
  forcing that second object into vibrational
  motion.
• Example pushing a swing
• Resonance is the cause of sound production in
  musical instruments.
• Energy is transferred thereby increasing the
  amplitude (volume) of the sound.

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Types of Resonance

• Resonance takes place in both closed pipe
  resonators and open pipe resonators.
• Resonance is achieved when there is a standing
  wave produced in the tube.
• Closed pipe resonators
• open end of tube is anti-node
• closed end of tube is node
• http//www2.biglobe.ne.jp/norimari/science/JavaEd
  /e-wave5.html
• Open pipe resonators
• both ends are open
• both ends are anti-nodes
• http//www2.biglobe.ne.jp/norimari/science/JavaEd
  /e-wave4.html

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Closed pipe resonator
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Harmonics of Closed Pipe Resonance

• The shortest column of air that can have a
  pressure anti-node at the closed end and a
  pressure node at the open end is ¼ wavelength
  long. This is called the fundamental frequency or
  first harmonic.
• As the frequency is increased, additional
  resonance lengths are found at ½ wavelength
  intervals.
• The frequency that corresponds to ¾ wavelength is
  called the 3rd harmonic, 5/4 wavelength is called
  the 5th harmonic, etc.

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Open pipe resonator
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Harmonics of Open Pipe Resonance

• The shortest column of air that can have nodes
  (or antinodes) at both ends is ½ wavelength long.
  This is called the fundamental frequency or first
  harmonic.
• As the frequency is increased, additional
  resonance lengths are found at ½ wavelength
  intervals.
• The frequency that corresponds to a full
  wavelength is the second harmonic, 3/2 wavelength
  is the third harmonic, etc.

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Problems

• 1. Matt is playing a toy flute, causing
  resonating waves in a open-end air column. The
  speed of sound through the air column is 336 m/s.
  The length of the air column is 30.0 cm.
  Calculate the frequency of the first, second, and
  third harmonics.

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Solution

• L ?/2
• 2 x L ?
• 2 x .30 .60 m
• v f ?
• 336 f (.60)
• f 560 Hz. (first harmonic)
• 2nd harmonic 560 560 1120 Hz.
• 3rd harmonic 1120 560 1680 Hz

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Problem

• 2. Tommy and the Test Tubes have a concert this
  weekend. The lead instrumentalist uses a test
  tube (closed end air column) with a 17.2 cm air
  column. The speed of sound in the test tube is
  340 m/s. Find the frequency of the first
  harmonic played by this instrument.

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Solution

• 2. L ?/4
• 4 x L ?
• 4 x .172 .688 m
• v f ?
• 340 f (.688)
• f 494 Hz

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SOUND INTENSITY

• THE LOUDNESS OF SOUND

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Sound Intensity

• The intensity of a sound is the amount of energy
  transported past a given area in a unit of time.
• Intensity power/area
• The greater the amplitude, the greater the rate
  at which energy is transported-the more intense
  the sound
• Intensity is inversely related to the square of
  the distance. As distance increases, the
  intensity decreases.

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Threshold of Hearing

• The human ear is sensitive to variations in
  pressure waves, that is, the amplitude of sound
  waves.
• The ear can detect wave amplitudes of 2x10-5 Pa
  up to 20 Pa.
• The amplitudes of these waves are measured on a
  logarithmic scale called sound level.
• Sound level is measured in decibels (dB).

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DECIBEL

• MEASURES THE LOUDNESS OF SOUND
• RELATES TO THE AMPLITUDE OF THE WAVE
• EVERY INCREASE OF 10dB HAS 10x GREATER AMPLITUDE

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A SOUND 10 TIMES AS INTENSE IS PERCEIVED AS BEING
ONLY TWICE AS LOUD
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NOISE POLLUTION

• Prolonged exposure to noise greater than 85-90
  dB may cause hearing loss
•   Brief exposures to noise sources of 100-130
  dB can cause hearing loss
• A single exposure to a level of 140 dB or
  higher can cause hearing loss

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EXPOSURE TO LOUD NOISE
Hours Per Day
Noise Level (dB)  
8 90
4 95
2 100
1 105
0.5 110
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Reducing Sound Intensity

• Cotton earplugs reduce sound intensity by
  approximately 10 dB.
• Special earplugs reduce intensity by 25 to 45 dB.
• Sound proof materials weakens the pressure
  fluctuations either by absorbing or reflecting
  the sound waves.
• When the sound waves are absorbed by soft
  materials, the energy is converted into thermal
  energy.

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Beats
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A beat occurs when sound waves of two different
(but very much alike) frequencies are played next
to each other. The result is constructive and
destructive interference at regular intervals.
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• This oscillation of wave amplitude is called a
  beat.
• The frequency of a beat is the magnitude of
  difference between the frequencies of the two
  waves, f ? fA fB ?
• See example problem 10 on p. 367.

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Anatomy of the Ear
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Sound starts at the Pinna
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Then goes through the auditory canal
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The sound waves will then vibrate the Tympanic
Membrane (eardrum) which is made of a thin layer
of skin.
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The tympanic membrane will then vibrate three
tiny bones the Malleus (hammer), the Incus
(anvil), and the Stapes (stirrup)
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The stapes will then vibrate the Cochlea
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Inside look of the Cochlea

• The stapes vibrates the cochlea
• The frequency of the vibrations will stimulate
  particular hairs inside the cochlea
• The intensity at which these little hairs are
  vibrated will determine how loud the sound is.
• The auditory nerve will then send this signal to
  the brain.

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