Sound Mark Lesmeister Dawson High School Physics This
presentation is intended solely for use by Dawson High School
Pre-AP Physics students.
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SECTION 1: INTRODUCTION TO SOUND
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Nature of Sound Waves Sound waves are the result of vibrating
molecules of air, water or other medium. Sound waves are
longitudinal waves. Animation courtesy Dan Russell, Kettering
University
Slide 5
Nature of Sound Waves Sound waves are the result of vibrating
molecules of air, water or other medium. Sound waves are
longitudinal waves. Motion of the medium is parallel to direction
of travel of the wave. Sound waves consist of compressions and
rarefactions. Compression Is to Rarefaction Crest Is to Trough High
density Is to Low density as
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Nature of Sound Waves Sound waves are the result of vibrating
molecules of air, water or other medium. Sound waves are
longitudinal waves. Sound waves spread out in three dimensions.
Animation courtesy Dan Russell, Kettering University
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Frequency of sound waves The frequency of an audible sound wave
is related to its pitch. Sound waves vary greatly in frequency.
Sound Waves Infrasonic 20 Hz 20,000 Hz
Use of Ultrasonic Waves Ultrasonic waves can be used to produce
ultrasound images of objects inside the body. These images do not
involve harmful X-rays. The size of the ultrasonic wavelength
limits the size of objects that can be seen.
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Warning: The next slide shows an image of a 28 weeks
gestational age fetus.
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4-d Ultrasound Image Source: Wikipedia
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PART 2: THE MATHEMATICS OF SOUND
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The Speed of Sound The speed of sound depends on the medium.
Animation courtesy Dan Russell, Kettering University
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The Speed of Sound The speed of sound depends on the medium.
The more rigid the medium, the faster sound travels through it. The
temperature of the medium may affect the speed of sound. The speed
of sound of some common materials is given on page 482. Air: 331
m/s at 0 o C, 346 m/s at 25 o C Water: 1490 m/s at 25 o C Metals:
Al- 5100 m/s, Cu- 3560 m/s
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Mach Numbers The speed of sound in air is also known as Mach 1.
A plane flying at Mach 2 is flying twice the speed of sound. The
shuttle flies at a speed of about Mach 25.
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Sound Application Questions: Marine Mammals Dolphins can
produce sound waves with frequencies from 250 Hz to 220 kHz, but
use only the higher frequencies for echolocation. Why? Dolphin
sound pulses travel through 20 o C ocean water at 1450 m/s, but
through 20 o C air at only 343 m/s. What explains the difference?
As a dolphin swims toward a fish, the frequency of the reflected
pulses is higher than the transmitted pulses. Is the dolphin
catching up to the fish or falling behind?
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Marine Mammal Discussion Question SONAR is the use of sound as
a means of detecting objects. Active SONAR systems send out pulses
of sound, the reflections of which are then received and
interpreted. Active sonar systems have been implicated in a small
number of strandings of marine mammals. Small means about 5
strandings per year (some of which involved more than in animal),
compared to 3,600 strandings/year from natural causes or 600,000
accidental deaths/year due to the commercial fishing industry.
Should peacetime use of SONAR be banned in order to prevent these
strandings?
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The Doppler Effect
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The Doppler Effect: Waves from a Moving Source v=f so a smaller
wavelength means a higher frequency. Animation courtesy Dan
Russell, Kettering University
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The Doppler Effect: Waves as seen by a moving observer.
Animation courtesy Dan Russell, Kettering University
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The Doppler Effect
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Motion of either the source or the observer of a wave causes
the frequency to shift. If the relative motion results in more wave
crests reaching the observer per second, the frequency is
increased. If the relative motion results in fewer wave crests
reaching the observer per second, the frequency is decreased.
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Calculating Doppler Effect: Moving Observer A moving observer
will detect additional wavefronts per second because of the
motion.
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Calculating the Doppler Effect: Moving Source dd
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Doppler Effect Use the upper signs when the objects are moving
toward each other, and the bottom signs when they are moving
away.
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Sound Intensity All waves transfer energy. Power is the rate of
energy transfer. Intensity is the rate of energy transfer through a
unit of area. In general, For a spherical wave, Courtesy of Dr. Dan
Russell, Kettering University 2008 by W.H. Freeman and Company
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Calculating Intensity P = power r = distance from the source.
Intensity is measured in W/m 2. What is the intensity of sound
waves from an electric guitar at a distance of 5.0 m when its power
output is 0.50 W? 1.6 x 10 -3 W/m 2
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Interpreting Intensity Intensity and frequency determine which
sounds are audible. The threshold of hearing has frequencies around
1000 Hz and intensities of 1.0 x10 -12 W/m 2. The threshold of pain
occurs at about 1.0 W/m 2. 1.0 x 10 -12 W/m 2 1.0 W/m 2
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Range of Hearing Diagram from Holt Physics, Holt, Reinhart and
Winston 2002.
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Loudness and Decibel level The intensity of a sound is related
to its loudness or volume. When intensity increases by a factor of
10, loudness approximately doubles. X 10 in intensity means X2 in
loudness. A decibel level relates the intensity of a sound to the
threshold of hearing intensity. The decibel scale is based on
powers of 10. X 10 in intensity means + 10 dB
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Decibel level dB LevelIncrease inApproximate Intensity loudness
increase 10 dB 10 X2 X 20100 X 4 X 301000 X8 X
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Table taken from Holt Physics, Holt, Reinhart and Winston
2002.
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Decibel Calculations Example 1: A certain loudspeaker doubles
the intensity of a sound wave. What is the corresponding dB
increase? Example 2: What is the intensity of a 75 dB sound wave if
the reference level is 10 -12 W/m 2 ?
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SOUND PHENOMENA
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Warm-up: Discovery Lab Activity Hold the tube vertically, so
that it is partially submerged in the water in the cup. Strike the
tuning fork and place it over the top of the tube. Slowly change
the position of the tube, up and down, and listen for any changes
in the sound.
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Resonance Many systems have a natural frequency of vibration;
for example Simple harmonic oscillators Pendulum Mass and spring
system Piano strings, other musical instruments. Resonance occurs
when the frequency of a force applied to a system matches the
natural frequency of vibration of the systems. A resonance will
result in a large amplitude of vibration.
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Standing Waves and Harmonics When certain systems, such as
strings or air columns, are vibrated, standing waves are produced.
Only standing waves of certain frequencies are possible. Those
frequencies are called harmonics of the system.
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Standing Waves on a String A stretched string will produce
harmonics with wavelengths that will fit on the string. If L is the
length of the string, the allowed wavelengths are 2L, L, (2/3)L,
(1/2)L, etc. Graphic from Holt Physics Holt, Reinhart and Winston
2002.
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Harmonic Series of Standing Waves: Vibrating String
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Standing Waves in an Air Column Standing waves can be set up in
an air column. A closed end of an air column will always be a node.
An open end of an air column will always be an antinode of a
standing wave.
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Harmonic Series of Standing Waves: Pipe Open at Both Ends
Graphic from Holt Physics Holt, Reinhart and Winston 2002. Flutes
and similar instruments are modeled as pipes open at both
ends.
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Harmonic Series of Standing Waves: Pipe Open at Both Ends
Graphic from Holt Physics Holt, Reinhart and Winston 2002.
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Harmonic Series: Pipe Closed at One End Graphic from Holt
Physics Holt, Reinhart and Winston 2002. Clarinets and brass
instruments can be modeled as pipes closed at one end.
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Harmonic Series: Pipe Closed at One End Graphic from Holt
Physics Holt, Reinhart and Winston 2002.
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Harmonics and Wind Instruments Other reed instruments such as
saxophones, oboes and bassoons, although they are closed at one
end, behave more like a cone than a cylinder. The result is that
their resonances are closer to a pipe open at both ends.
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Harmonics and Timbre Sounds with the same frequency can sound
quite different. The difference is the result of the presence of
different harmonics at different intensities. The characteristics
of a musical note that result from the different harmonics it
contains are called timbre. The fundamental frequency determines
the pitch of the sound.
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Sample Timbres 440 Hz tone 440 Hz and 880 Hz First 5 harmonics
of 440 Hz, each with intensity of previous one. First 5 odd
harmonics of 440 Hz, each with intensity of previous one. Clarinet
playing scale.
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Beats Sound waves of slightly different frequencies produce
beats. 440 Hz and 441 Hz together Beats are the result of
constructive and destructive interference. The frequency of the
beats is equal to the difference in frequency of the two sound
waves. 440 Hz and 442 Hz together.
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Some Musical Intervals Unison- e.g. middle C and middle C A
note with the same frequency. Octave- e.g. middle C and high C A
note with double the frequency. The first harmonic of this note
equals the second harmonic of the original note. Fifth- e.g. C and
G A note with 3/2 the frequency. The second harmonic of this note
equals the 3 rd harmonic of the original note. Fourth- e.g. C and F
A note with 4/3 the frequency. The third harmonic of this note
equals the fourth harmonic of the original note.