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Sounds of music study guide
Sound is amechanical wavethat results from the back and forth vibration of theparticles of the medium through which the sound wave is moving. If a sound wave ismoving from left to right through air, then particles of air will be displaced both
rightward and leftward as the energy of the sound wave passes through it. The motionof the particles is parallel (and anti-parallel) to the direction of the energy transport.This is what characterizes sound waves in air aslongitudinal waves.
A vibrating tuning fork is capable of creating such a longitudinal wave. As the tines of
the fork vibrate back and forth, they push on neighboring air particles. The forward
motion of a tine pushes air molecules horizontally to the right and the backward
retraction of the tine creates a low-pressure area allowing the air particles to move back
to the left.
Because of the longitudinal motion of the air particles, there are regions in the air
where the air particles are compressed together and other regions where the air
particles are spread apart. These regions are known
as compressionsand rarefactionsrespectively. The compressions are regions of high
air pressure while the rarefactions are regions of low air pressure. The diagram below
depicts a sound wave created by a tuning fork and propagated through the air in an
open tube. The compressions and rarefactions are labeled.
The wavelengthof a wave is merely the distance that a disturbance travels along the
medium in one complete wave cycle. Since a wave repeats its pattern once every wave
cycle, the wavelength is sometimes referred to as the length of the repeating patterns -
the length of one complete wave. For a transverse wave, this length is commonly
measured from one wave crest to the next adjacent wave crest or from one wave
trough to the next adjacent wave trough. Since a longitudinal wave does not contain
crests and troughs, its wavelength must be measured differently. A longitudinal wave
consists of a repeating pattern of compressions and rarefactions. Thus, the wavelength
is commonly measured as the distance from one compression to the next adjacent
compression or the distance from one rarefaction to the next adjacent rarefaction.
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Since a sound wave consists of a repeating pattern of high-pressure and low-pressure
regions moving through a medium, it is sometimes referred to as a pressure wave. If
a detector, whether it is the human ear or a man-made instrument, were used to detect
a sound wave, it would detect fluctuations in pressure as the sound wave impinges
upon the detecting device. At one instant in time, the detector would detect a high
pressure; this would correspond to the arrival of a compression at the detector site. At
the next instant in time, the detector might detect normal pressure. And then finally a
low pressure would be detected, corresponding to the arrival of a rarefaction at the
detector site. The fluctuations in pressure as detected by the detector occur at periodic
and regular time intervals. In fact, a plot of pressure versus time would appear as a
sine curve. The peak points of the sine curve correspond to compressions; the low
points correspond to rarefactions; and the "zero points" correspond to the pressure that
the air would have if there were no disturbance moving through it. The diagram below
depicts the correspondence between the longitudinal nature of a sound wave in air and
the pressure-time fluctuations that it creates at a fixed detector location.
The above diagram can be somewhat misleading if you are not careful. The
representation of sound by a sine wave is merely an attempt to illustrate the sinusoidal
nature of the pressure-time fluctuations. Do not conclude that sound is a transverse
wave that has crests and troughs. Sound waves traveling through air are indeed
longitudinal waves with compressions and rarefactions. As sound passes through air (or
any fluid medium), the particles of air do not vibrate in a transverse manner. Do not be
misled - sound waves traveling through air are longitudinal waves.
Atransverse waveis a wave in which the particles of the medium are displaced in a
direction perpendicular to the direction of energy transport. A transverse wave can be
created in a rope if the rope is stretched out horizontally and the end is vibrated back-
and-forth in a vertical direction. If a snapshot of such a transverse wave could be taken
so as to freezethe shape of the rope in time, then it would look like the following
diagram.
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The dashed line drawn through the center of the diagram represents theequilibrium or
rest positionof the string. This is the position that the string would assume if there
were no disturbance moving through it. Once a disturbance is introduced into the string,
the particles of the string begin to vibrate upwards and downwards. At any given
moment in time, a particle on the medium could be above or below the rest position.
Points A, E and H on the diagram represent the crests of this wave. The crestof a
wave is the point on the medium that exhibits the maximum amount of positive or
upward displacement from the rest position. Points C and J on the diagram represent
the troughs of this wave. Thetroughof a wave is the point on the medium thatexhibits the maximum amount of negative or downward displacement from the rest
position.
The wave shown above can be described by a variety of properties. One such property
is amplitude. The amplitudeof a wave refers to the maximum amount of displacement
of a particle on the medium from its rest position. In a sense, the amplitude is the
distancefrom rest to crest. Similarly, the amplitude can be measured from the rest
position to the trough position. In the diagram above, the amplitude could be measured
as the distance of a line segment that is perpendicular to the rest position and extends
vertically upward from the rest position to point A.
The wavelength is another property of a wave that is portrayed in the diagram above.
The wavelengthof a wave is simply the length of one complete wave cycle. If you
were to trace your finger across the wave in the diagram above, you would notice that
your finger repeats its path. A wave is a repeating pattern. It repeats itself in a periodic
and regular fashion over both time and space. And the length of one such spatial
repetition (known as a wave cycle) is the wavelength. The wavelength can be
measured as the distance from crest to crest or from trough to trough. In fact, the
wavelength of a wave can be measured as the distance from a point on a wave to the
corresponding point on the next cycle of the wave. In the diagram above, the
wavelength is the horizontal distance from A to E, or the horizontal distance from B to F,or the horizontal distance from D to G, or the horizontal distance from E to H. Any one
of these distance measurements would suffice in determining the wavelength of this
wave.
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Alongitudinal waveis a wave in which the particles of the medium are displaced in a
direction parallel to the direction of energy transport. A longitudinal wave can be
created in a slinky if the slinky is stretched out horizontally and the end coil is vibrated
back-and-forth in a horizontal direction. If a snapshot of such a longitudinal wave could
be taken so as to freezethe shape of the slinky in time, then it would look like the
following diagram.
Because the coils of the slinky are vibrating longitudinally, there are regions where they
become pressed together and other regions where they are spread apart. A region
where the coils are pressed together in a small amount of space is known as acompression. Acompressionis a point on a medium through which a longitudinal
wave is traveling that has the maximum density. A region where the coils are spread
apart, thus maximizing the distance between coils, is known as a rarefaction.
A rarefactionis a point on a medium through which a longitudinal wave is traveling
that has the minimum density. Points A, C and E on the diagram above represent
compressions and points B, D, and F represent rarefactions. While a transverse wave
has an alternating pattern of crests and troughs, a longitudinal wave has an alternating
pattern of compressions and rarefactions.
As discussed above, thewavelengthof a wave is the length of one complete cycle of a
wave. For a transverse wave, the wavelength is determined by measuring from crest to
crest. A longitudinal wave does not have crest; so how can its wavelength be
determined? The wavelength can always be determined by measuring the distance
between any two corresponding points on adjacent waves. In the case of a longitudinal
wave, a wavelength measurement is made by measuring the distance from a
compression to the next compression or from a rarefaction to the next rarefaction. On
the diagram above, the distance from point A to point C or from point B to point D
would be representative of the wavelength.
A sound wave, like any other wave, is introduced into a medium by a vibrating object.
The vibrating object is the source of the disturbance that moves through the medium.
The vibrating object that creates the disturbance could be the
vocal cords of a person, the vibrating string and sound board of
a guitar or violin, the vibrating tines of a tuning fork, or the
vibrating diaphragm of a radio speaker. Regardless of what
vibrating object is creating the sound wave, the particles of the medium through which
the sound moves is vibrating in a back and forth motion at a given frequency.
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Thefrequency of a waverefers to how often the particles of the medium vibrate when a
wave passes through the medium. The frequency of a wave is measured as the number
of complete back-and-forth vibrations of a particle of the medium per unit of time. If a
particle of air undergoes 1000longitudinal vibrationsin 2 seconds, then the frequency
of the wave would be 500 vibrations per second. A commonly used unit for frequency is
the Hertz (abbreviated Hz), where
1 Hertz = 1 vibration/second
As a sound wave moves through a medium, each particle of the medium vibrates at the
same frequency. This is sensible since each particle vibrates due to the motion of its
nearest neighbor. The first particle of the medium begins vibrating, at say 500 Hz, and
begins to set the second particle into vibrational motion at the same frequency of 500
Hz. The second particle begins vibrating at 500 Hz and thus sets the third particle of the
medium into vibrational motion at 500 Hz. The process continues throughout the
medium; each particle vibrates at the same frequency. And of course the frequency at
which each particle vibrates is the same as the frequency of the original source of thesound wave. Subsequently, a guitar string vibrating at 500 Hz will set the air particles in
the room vibrating at the same frequency of 500 Hz, which carries a sound signalto the
ear of a listener, which is detected as a 500 Hz sound wave.
The back-and-forth vibrational motion of the particles of the medium would not be the
only observable phenomenon occurring at a given frequency. Since a sound wave is
apressure wave,a detector could be used to detect oscillations in pressure from a high
pressure to a low pressure and back to a high pressure. As the compressions (high
pressure) and rarefactions (low pressure) move through the medium, they would reach
the detector at a given frequency. For example, a compression would reach thedetector 500 times per second if the frequency of the wave were 500 Hz. Similarly, a
rarefaction would reach the detector 500 times per second if the frequency of the wave
were 500 Hz. The frequency of a sound wave not only refers to the number of back-
and-forth vibrations of the particles per unit of time, but also refers to the number of
compressions or rarefactions that pass a given point per unit of time. A detector could
be used to detect the frequency of these pressure oscillations over a given period of
time. The typical output provided by such a detector is a pressure-time plot as shown
below.
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Since a pressure-time plot shows the fluctuations in pressure over time, theperiodof
the sound wave can be found by measuring the time between successive high pressure
points (corresponding to the compressions) or the time between successive low
pressure points (corresponding to the rarefactions).As discussed in an earlier unit,the
frequency is simply the reciprocal of the period. For this reason, a sound wave with a
high frequency would correspond to a pressure time plot with a small period - that is, a
plot corresponding to a small amount of time between successive high pressure points.
Conversely, a sound wave with a low frequency would correspond to a pressure time
plot with a large period - that is, a plot corresponding to a large amount of time
between successive high pressure points. The diagram below shows two pressure-time
plots, one corresponding to a high frequency and the other to a low frequency.
The ears of a human (and other animals) are sensitive detectors capable of detecting
the fluctuations in air pressure that impinge upon the eardrum. The mechanics of the
ear's detection ability will be discussedlater in this lesson.For now, it is sufficient to say
that the human ear is capable of detecting sound waves with a wide range of
frequencies, ranging between approximately 20 Hz to 20 000 Hz. Any sound with a
frequency below the audible range of hearing (i.e., less than 20 Hz) is known as
an infrasoundand any sound with a frequency above the audible range of hearing
(i.e., more than 20 000 Hz) is known as an ultrasound. Humans are not alone in their
ability to detect a wide range of frequencies. Dogs can detect frequencies as low as
approximately 50 Hz and as high as 45 000 Hz. Cats can detect frequencies as low as
approximately 45 Hz and as high as 85 000 Hz. Bats, being nocturnal creature, must
rely on sound echolocation for navigation and hunting. Bats can detect frequencies ashigh as 120 000 Hz. Dolphins can detect frequencies as high as 200 000 Hz. While dogs,
cats, bats, and dolphins have an unusual ability to detect ultrasound, an elephant
possesses the unusual ability to detect infrasound, having an audible range from
approximately 5 Hz to approximately 10 000 Hz.
The sensation of a frequency is commonly referred to as the pitchof a sound. A high
pitch sound corresponds to a high frequency sound wave and a low pitch sound
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corresponds to a low frequency sound wave. Amazingly, many people, especially those
who have been musically trained, are capable of detecting a difference in frequency
between two separate sounds that is as little as 2 Hz. When two sounds with a
frequency difference of greater than 7 Hz are played simultaneously, most people are
capable of detecting the presence of a complex wave pattern resulting from
theinterferenceandsuperpositionof the two sound waves. Certain sound waves when
played (and heard) simultaneously will produce a particularly pleasant sensation when
heard, are said to beconsonant. Such sound waves form the basis of intervalsin
music. For example, any two sounds whose frequencies make a 2:1 ratio are said to be
separated by an octaveand result in a particularly pleasing sensation when heard. That
is, two sound waves sound good when played together if one sound has twice the
frequency of the other. Similarly two sounds with a frequency ratio of 5:4 are said to be
separated by an interval of a third; such sound waves also sound good when played
together. Examples of other sound wave intervals and their respective frequency ratios
are listed in the table below.Interval Frequency Ratio ExamplesOctave 2:1 512 Hz and 256 Hz
Third 5:4 320 Hz and 256 HzFourth 4:3 342 Hz and 256 Hz
Fifth 3:2 384 Hz and 256 Hz
The ability of humans to perceive pitch is associated with the frequency of the sound
wave that impinges upon the ear. Because sound waves traveling through air are
longitudinal waves that produce high- and low-pressure disturbances of the particles of
the air at a given frequency, the ear has an ability to detect such frequencies and
associate them with the pitch of the sound. But pitch is not the only property of a
sound wave detectable by the human ear.
Sound waves are introduced into a medium by the vibration of an object. For example,
a vibrating guitar string forces surrounding air molecules to be compressed and
expanded, creating a pressure disturbance consisting
of an alternating pattern ofcompressions and
rarefactions.The disturbance then travels from particle
to particle through the medium, transporting energy as
it moves. The energy that is carried by the disturbancewas originally imparted to the medium by the vibrating
string. The amount of energy that is transferred to the
medium is dependent upon the amplitude of vibrations
of the guitar string. If more energy is put into the plucking of the string (that is,
moreworkis done to displace the string a greater amount from its rest position), then
the string vibrates with a greater amplitude. The greater amplitude of vibration of the
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guitar string thus imparts more energy to the medium, causing air particles to be
displaced a greater distance from their rest position. Subsequently, the amplitude of
vibration of the particles of the medium is increased, corresponding to an increased
amount of energy being carried by the particles. Thisrelationship between energy and
amplitudewas discussed in more detail in a previous unit.
Sound Intensity and Distance
The amount of energy that is transported past a given area of the medium per unit of
time is known as the intensityof the sound wave. The greater the amplitude of
vibrations of the particles of the medium, the greater the rate at which energy is
transported through it, and the more intense that the sound wave is. Intensity is the
energy/time/area; and since the energy/time ratio is equivalent to the quantitypower,
intensity is simply the power/area.
Typical units for expressing the intensity of a sound wave are Watts/meter 2.
As a sound wave carries its energy through a two-dimensional or three-dimensional
medium, the intensity of the sound wave decreases with increasing distance from the
source. The decrease in intensity with increasing distance is
explained by the fact that the wave is spreading out over a
circular (2 dimensions) or spherical (3 dimensions) surface and
thus the energy of the sound wave is being distributed over a
greater surface area. The diagram at the right shows that thesound wave in a 2-dimensional medium is spreading out in space
over a circular pattern. Since energy is conserved and the area
through which this energy is transported is increasing, the power
(being a quantity that is measured on a per areabasis) must
decrease.
The mathematical relationship between intensity and distance is sometimes referred to
as an inverse square relationship. The intensity varies inversely with the square of
the distance from the source. So if the distance from the source is doubled (increased
by a factor of 2), then the intensity is quartered (decreased by a factor of 4). Similarly,
if the distance from the source is quadrupled, then the intensity is decreased by a factor
of 16. Applied to the diagram at the right, the intensity at point B is one-fourth the
intensity as point A and the intensity at point C is one-sixteenth the intensity at point A.
Since the intensity-distance relationship is an inverse relationship, an increase in one
quantity corresponds to a decrease in the other quantity. And since the intensity-
distance relationship is an inverse square relationship, whatever factor by which the
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distance is increased, the intensity is decreased by a factor equal to the square of
the distance change factor. The sample data in the table below illustrate the inverse
square relationship between power and distance.
Distance Intensity1 m 160 units
2 m 40 units3 m 17.8 units
4 m 10 units
The Threshold of Hearing and the Decibel Scale
Humans are equipped with very sensitive ears capable of detecting sound waves of
extremely low intensity. The faintest sound that the typical human ear can detect hasan intensity of 1*10-12W/m2. This intensity corresponds to a pressure wave in which a
compression of the particles of the medium increases the air pressure in that
compressional region by a mere 0.3 billionth of an atmosphere. A sound with an
intensity of 1*10-12W/m2corresponds to a sound that will displace particles of air by a
mere one-billionth of a centimeter. The human ear can detect such a sound. WOW!
This faintest sound that a human ear can detect is known as the threshold of hearing.
The most intense sound that the ear can safely detect without suffering any physical
damage is more than one billion times more intense than the threshold of hearing.
Since the range of intensities that the human ear can detect is so large, the scale that is
frequently used by physicists to measure intensity is a scale based on powers of 10.
This type of scale is sometimes referred to as a logarithmic scale. The scale for
measuring intensity is the decibel scale. The threshold of hearing is assigned a sound
level of 0 decibels (abbreviated 0 dB); this sound corresponds to an intensity of 1*10 -
12W/m2. A sound that is 10 times more intense ( 1*10 -11W/m2) is assigned a sound level
of 10 dB. A sound that is 10*10 or 100 times more intense (1*10-10W/m2) is assigned a
sound level of 20 db. A sound that is 10*10*10 or 1000 times more intense (1*10-
9W/m2) is assigned a sound level of 30 db. A sound that is 10*10*10*10 or 10000
times more intense (1*10-8W/m2) is assigned a sound level of 40 db. Observe that this
scale is based on powers of 10. If one sound is 10x
times more intense than anothersound, then it has a sound level that is 10*x more decibels than the less intense sound.
The table below lists some common sounds with an estimate of their intensity and
decibel level.
Source Intensity Intensity Level# of Times
Greater Than TOHThreshold of Hearing (TOH) 1*10-12W/m2 0 dB 100
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Rustling Leaves 1*10-11W/m2 10 dB 101
Whisper 1*10-10W/m2 20 dB 102
Normal Conversation 1*10-6W/m2 60 dB 106Busy Street Traffic 1*10-5W/m2 70 dB 107
Vacuum Cleaner 1*10-4W/m2 80 dB 108
Large Orchestra 6.3*10-3
W/m2
98 dB 109.8
Walkman at Maximum Level 1*10-2W/m2 100 dB 1010Front Rows of Rock Concert 1*10-1W/m2 110 dB 1011
Threshold of Pain 1*101W/m2 130 dB 1013
Military Jet Takeoff 1*102W/m2 140 dB 1014Instant Perforation of Eardrum 1*104W/m2 160 dB 1016
A sound wave is apressure disturbancethat travels through a medium by means of
particle-to-particle interaction. As one particle becomes disturbed, it exerts a force on
the next adjacent particle, thus disturbing that particle from rest and transporting the
energy through the medium. Like any wave, thespeed of asound waverefers to how fast the disturbance is passed from
particle to particle. Whilefrequencyrefers to the number of
vibrations that an individual particle makes per unit of time,
speed refers to the distance that the disturbance travels per unit of time. Always be
cautious to distinguish between the two often-confused quantities of speed (how fast...)
and frequency (how often...).
Since the speed of a wave is defined as the distance that a point on a wave (such as a
compression or a rarefaction) travels per unit of time, it is often expressed in units of
meters/second (abbreviated m/s). In equation form, this is
speed = distance/time
The faster a sound wave travels, the more distance it will cover in the same period of
time. If a sound wave were observed to travel a distance of 700 meters in 2 seconds,
then the speed of the wave would be 350 m/s. A slower wave would cover less distance
- perhaps 660 meters - in the same time period of 2 seconds and thus have a speed of
330 m/s. Faster waves cover more distance in the same period of time.
Factors Affecting Wave Speed
The speed of any wavedepends upon the properties of the mediumthrough which the
wave is traveling. Typically there are two essential types of properties that effect wave
speed - inertial properties and elastic properties. Elastic propertiesare those
properties related to the tendency of a material to maintain its shape and not deform
whenever a force or stress is applied to it. A material such as steel will experience a
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very small deformation of shape (and dimension) when a stress is applied to it. Steel is
a rigid material with a high elasticity. On the other hand, a material such as a rubber
band is highly flexible; when a force is applied to stretch the rubber band, it deforms or
changes its shape readily. A small stress on the rubber band causes a large deformation.
Steel is considered to be a stiff or rigid material, whereas a rubber band is considered a
flexible material. At the particle level, a stiff or rigid material is characterized by atoms
and/or molecules with strong attractions for each other. When a force is applied in an
attempt to stretch or deform the material, its strong particle interactions prevent this
deformation and help the material maintain its shape. Rigid materials such as steel are
considered to have a high elasticity. (Elastic modulus is the technical term). The phase
of matter has a tremendous impact upon the elastic properties of the medium. In
general, solids have the strongest interactions between particles, followed by liquids
and then gases. For this reason, longitudinal sound waves travel faster in solids than
they do in liquids than they do in gases. Even though the inertial factor may favor gases,
the elastic factor has a greater influence on the speed (v) of a wave, thus yielding thisgeneral pattern:
vsolids> vliquids> vgases
Inertial properties are those properties related to the material's tendency to be sluggish
to changes in its state of motion. The density of a medium is an example of an inertial
property. The greater the inertia (i.e., mass density) of individual particles of the
medium, the less responsive they will be to the interactions between neighboring
particles and the slower that the wave will be. As stated above, sound waves travel
faster in solids than they do in liquids than they do in gases. However, within a single
phase of matter, the inertial property of density tends to be the property that has a
greatest impact upon the speed of sound. A sound wave will travel faster in a less
dense material than a more dense material. Thus, a sound wave will travel nearly three
times faster in Helium than it will in air. This is mostly due to the lower mass of Helium
particles as compared to air particles.
The speed of a sound wave in air depends upon the properties of the air, mostly the
temperature, and to a lesser degree, the humidity. Humidity is the result of water vapor
being present in air. Like any liquid, water has a tendency to evaporate. As it does,
particles of gaseous water become mixed in the air. This additional matter will affect
the mass density of the air (an inertial property). The temperature will affect the
strength of the particle interactions (an elastic property). At normal atmosphericpressure, the temperature dependence of the speed of a sound wave through dry airis
approximated by the following equation:
v = 331 m/s + (0.6 m/s/C)T
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where T is the temperature of the air in degrees Celsius. Using this equation to
determine the speed of a sound wave in air at a temperature of 20 degrees Celsius
yields the following solution.
v = 331 m/s + (0.6 m/s/C)T
v = 331 m/s + (0.6 m/s/C)(20 C)
v = 331 m/s + 12 m/s
v = 343 m/s
(The above equation relating the speed of a sound wave in air to the temperature
provides reasonably accurate speed values for temperatures between 0 and 100 Celsius.
The equation itself does not have any theoretical basis; it is simply the result of
inspecting temperature-speed data for this temperature range. Other equations do exist
that are based upon theoretical reasoning and provide accurate data for all
temperatures. Nonetheless, the equation above will be sufficient for our use as
introductory Physics students.)
Human hearing relies on the ability of the ear and the neural system to sense andprocess variations in sound pressure. Accordingly, the act of hearing has bothsubconscious and conscious effects. Subconscious effects, such as hearing loss, aredue to prolonged exposure to high sound pressure levels. Conscious effects are adirect result of the ears' acute response to a sound and how the cognitive part ofthe brain evaluates the sound. An example of an acute response to a sound is thepain and resultant ringing felt in the ear when a whistle is blown close to the ear inan enclosed environment. An example of utilizing conscious response is using soundto convey information to consumers, such as designing a product to emit sounds
that indicate operation and/or status. Psychoacoustics is the field of study thatseeks to better understand our perception of sound by investigating its consciouseffects.
For speech and music, the verbal content conveys much of the information.Furthermore, for speech, music, and many other sounds, the physicalcharacteristics of the sound produce hearing sensations in the listener. The tablebelow lists three primary physical characteristics of sound and their correspondinghearing sensations.
Physical Characteristic Hearing Sensation
Sound Pressure Level Loudness
Frequency Pitch
Duration Subjective Duration
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These three hearing sensations directly correlate with their corresponding physicalcharacteristic. However, human hearing is a complex system and many sensationsdo not correlate directly to one physical characteristic. For example, in the tableabove, the sensation of pitch is also dependent on the sound pressure level.
Much of the challenge in the field of psychoacoustics stems from the fact that
different listeners perceive identical sounds differently. Differences in age, gender,nationality, and many other factors affect human perception. In addition to thischallenge of a heterogeneous population, consumer expectations are different fordifferent types of products they purchase. For example, a customer expectsdifferent sound characteristics from motorcycles, dishwashers, and personalcomputers. Therefore, sound quality evaluations are usually specific to the type ofproduct and the target consumer.
Because hearing is one of the integral processes through which humans receiveinformation and because the sound of a product carries so much information, thereis significant, ongoing research to classify hearing sensations and correlate thesesensations to physical characteristics of the signal. Through ongoing investigation,
researchers continue to identify physical characteristics of interest and proposeimproved objective sound quality metrics that correlate better to human perception.
Physiology of Human Hearing
The ear is an organ that receives audible information and transmits that sound tothe neural system, which results in auditory sensations. However, the body of thelistener distorts the sound field. Researchers can measure the resultant change inthe sound field by calculating the difference between the sound pressure level inthe free field and the sound pressure level in the ear canal of the listener. The bodyof the listener changes the sound field the most for frequencies below 1.5 kHz.
Scientists typically divide the human ear into three main regions: the outer ear, the
middle ear, and the inner ear. The following figure shows a diagram of the humanear.
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The outer ear canal, because of its shape and length, is responsible for the highsensitivity to sounds with frequency components around 4 kHz. The middle eartransfers sound energy from the oscillations of air particles in the outer ear to
oscillations in the fluids within the inner ear. The middle ear system acts like atransformer, matching the acoustic impedance between the air and the fluids atfrequencies centered at 1 kHz. The inner ear transmits the fluid oscillations to thecorti on the basilar membrane, where sensory cells convert the fluid oscillations tosignals that the nervous system can process. The inner ear also can separatefrequencies, because different frequencies produce maximum oscillations atdifferent positions along the basilar membrane.
Limits of Hearing
The ear is a very sophisticated auditory organ and can be thought of as a complexinstrument for auditory signals. Human hearing can detect small variations in airpressure, ranging from 10 Pa up to 100 Pa. The detection of these small variations
occurs in the presence of atmospheric pressure, where 1 atm = 101.3 kPa.Furthermore, humans perceive loudness on a logarithmic scale. The internationalstandard reference for sound pressure level measurements is 20 Pa (0 dB), whichis the threshold of quiet. This is considered the nominal threshold of hearing,although approximately half of the general population can sense sounds at evenlower levels. On the opposite end of sound pressure level measurements, humans
experience discomfort and pain from sounds with sound pressure levels greaterthan 100 Pa (134 dB). Within this range in level, humans can typically discernchanges as small as 1 dB.
Human hearing can detect frequencies between 20 Hz and 20 kHz. Frequencycomponents outside this range are not generally considered to impact the humanperception of sound, regardless of the sound pressure level. As explained in theprevious section, there are physical reasons why human hearing is most sensitiveto frequency components around 1 kHz and 4 kHz. Many studies have
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demonstrated the sensitivity of the ear as a function of frequency, which is typicallyplotted in equal loudness curves as in the following figure.1
Besides the sound pressure level-dependent sensitivity of hearing, humans also candifferentiate very fine changes in frequency. Below frequencies of 500 Hz, the ear
can differentiate tone bursts with a frequency difference of approximately 1 Hz.Above 500 Hz, the barely-noticeable difference is proportional to the frequency(0.002 x f).
Masking
Masking describes the phenomenon in which a sound becomes imperceptible due tothe presence of another sound. An example of this phenomenon is when loud musicmasks the sound of emergency sirens, or when a background noise partially masks
conversational speech. The transition between an unmasked tone and a completelymasked tone is continuous. The masked threshold is the sound pressure level of abarely-audible test tone in the presence of a masking sound.
Time Masking
Simultaneous masking describes the effect when the masked signal and the
masking signal occur at the same time. Human hearing is sensitive to the temporalstructure of sound, and masking also can occur between sounds that are notpresent simultaneously. Pre-masking is when the test tone occurs before themasking sound. Post-masking is when the test tone occurs after the masking sound.The following figure shows the time regions of pre-masking, simultaneous masking,and post-masking in relation to the masking signal.
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Post-masking is a pronounced phenomenon that corresponds to decay in the effectof the masking signal. Pre-masking is a more subtle effect caused by the fact thathearing does not occur instantaneously because sounds require some time to sense.As indicated in the figure above, researchers typically can measure pre-masking foronly about 20 ms. Post-masking is the more dominant temporal effect and can bemeasured for 100 ms following the cessation of the masking sound. Both thethreshold in quiet and the masked threshold depend on the duration of the testtone. Researchers must know these dependencies when investigating pre- andpost-masking because they use short-duration test signals to perform thesemeasurements.
Frequency Masking
Broadband white noise can mask test tones. White noise has a spectral density thatis independent of frequency. Other types of noise and signals, such as pink noise,narrow-band noise, pure tones, and complex tones, also can mask a test signal.When narrow-band noise is the masking signal, masked thresholds show a verysteep rise greater than 100 dB per decade as the test tone increases in frequency
up to the center frequency of the narrow-band noise. This test tone increase isindependent of the level of the masking noise. For frequencies greater than thecenter frequency of the noise, the masked threshold decreases quickly for lowlevels of masking noise but more slowly for high levels of masking noise. Whenpure tones are the masking signal, the signal needs additional filters to removemeasurement artifacts such as audible beating and difference tones. The followingfigure shows the masked threshold for a masking signal at a frequency of 1 kHz.
Guitara stringed instrument usually having six strings
Octave
a set of 8 notes
Fiftha set of 5 notes
Fourtha set of 4 notes
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Thirda set of 3 notes
Seconda set of 2 notes
Sixtha set of 6 notes
Seventha set of 7 notes
Node
a place where no sound waves are generated
Theme Movement #2 New World Symphonythe required piece for 2013 Science Olympiad
Sound Wavea wave that transmits sound
Standing wavea wave (as a sound wave in a chamber or an
electromagnetic wave in a transmission line) inwhich the ratio of its instantaneous amplitude atone point to that at any other point does not vary
with time
HertzThe unit of frequency
Percussion InstrumentAn instrument that you pound on a piece tomake it generate sound waves.
Wind InstrumentAn instrument that you blow into to make sound
Brass InstrumentAn wind instrument made of brass
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String Instrument
An instrument that uses string vibrations tocreate sound waves.
Pitchthe property of sound that varies with variationin the frequency of vibration
Speed of SoundThe speed at which a sound wave travels (340.29meters per second at sea level)
Timbrethe distinctive property of a complex sound
Wave interferenceis the phenomenon that occurs when two waves meet whiletraveling along the same medium. The interference of waves causes the medium to
take on a shape that results from the net effect of the two individual waves upon the
particles of the medium. As mentioned ina previous unitof The Physics Classroom
Tutorial, if two upward displaced pulses having the same shape meet up with one
another while traveling in opposite directions along a medium, the medium will take on
the shape of an upward displaced pulse with twice the amplitude of the two interfering
pulses. This type of interference is known as constructive interference. If an upward
displaced pulse and a downward displaced pulse having the same shape meet up with
one another while traveling in opposite directions along a medium, the two pulses will
cancel each other's effect upon the displacement of the medium and the medium will
assume the equilibrium position. This type of interference is known as destructive
interference. The diagrams below show two waves - one is blue and the other is red -
interfering in such a way to produce a resultant shape in a medium; the resultant is
shown in green. In two cases (on the left and in the middle), constructive interference
occurs and in the third case (on the far right, destructive interference occurs.
But how can sound waves that do not possess upward and downward displacements
interfere constructively and destructively? Sound is a pressure wave that consists
ofcompressionsandrarefactions.As a compression passes through a section of a
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medium, it tends to pull particles together into a small region of space, thus creating a
high-pressure region. And as a rarefaction passes through a section of a medium, it
tends to push particles apart, thus creating a low-pressure region. The interference of
sound waves causes the particles of the medium to behave in a manner that reflects
the net effect of the two individual waves upon the particles. For example, if a
compression (high pressure) of one wave meets up with a compression (high pressure)
of a second wave at the same location in the medium, then the net effect is that that
particular location will experience an even greater pressure. This is a form of
constructive interference. If two rarefactions (two low-pressure disturbances) from two
different sound waves meet up at the same location, then the net effect is that that
particular location will experience an even lower pressure. This is also an example of
constructive interference. Now if a particular location along the medium repeatedly
experiences the interference of two compressions followed up by the interference of
two rarefactions, then the two sound waves will continually reinforceeach other and
produce a very loud sound. The loudness of the sound is the result of the particles atthat location of the medium undergoing oscillations from very high to very low
pressures. As mentioned ina previous unit,locations along the medium where
constructive interference continually occurs are known as anti-nodes. The animation
below shows two sound waves interfering constructively in order to produce very large
oscillations in pressure at a variety of anti-nodal locations. Note that compressions are
labeled with a C and rarefactions are labeled with an R.
Now if two sound waves interfere at a given location in such a way that the
compression of one wave meets up with the rarefaction of a second wave, destructive
interference results. The net effect of a compression (which pushes particles together)
and a rarefaction (which pulls particles apart) upon the particles in a given region of the
medium is to not even cause a displacement of the particles. The tendency of the
compression to push particles together is canceled by the tendency of the rarefactions
to pull particles apart; the particles would remain at their rest position as though there
wasn't even a disturbance passing through them. This is a form of destructive
interference. Now if a particular location along the medium repeatedly experiences the
interference of a compression and rarefaction followed up by the interference of ararefaction and a compression, then the two sound waves will continually canceleach
other and no sound is heard. The absence of sound is the result of the particles
remaining at rest and behaving as though there were no disturbance passing through it.
Amazingly, in a situation such as this, two sound waves would combine to produce no
sound. As mentioned ina previous unit,locations along the medium where destructive
interference continually occurs are known as nodes.
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Two Source Sound Interference
A popular Physics demonstration involves the interference of two sound waves from two
speakers. The speakers are set approximately 1-meter apart and produced identical
tones. The two sound waves traveled through the air in front of the speakers, spreading
our through the room in spherical fashion. A snapshot in time of the appearance of
these waves is shown in the diagram below. In the diagram, the compressions of a
wavefront are represented by a thick line and the rarefactions are represented by thin
lines. These two waves interfere in such a manner as to produce locations of some loud
sounds and other locations of no sound. Of course the loud sounds are heard at
locations where compressions meet compressions or rarefactions meet rarefactions and
the "no sound" locations appear wherever the compressions of one of the waves meet
the rarefactions of the other wave. If you were to plug one ear and turn the other ear
towards the place of the speakers and then slowly walk across the room parallel to theplane of the speakers, then you would encounter an amazing phenomenon. You would
alternatively hear loud sounds as you approached anti-nodal locations and virtually no
sound as you approached nodal locations. (As would commonly be observed, the nodal
locations are not true nodal locations due to reflections of sound waves off the walls.
These reflections tend to fill the entire room with reflected sound. Even though the
sound waves that reach the nodal locations directly from the speakers destructively
interfere, other waves reflecting off the walls tend to reach that same location to
produce a pressure disturbance.)
Destructive interference of sound waves becomes an important issue in the design ofconcert halls and auditoriums. The rooms must be designed in such as way as to
reduce the amount of destructive interference. Interference can occur as the result of
sound from two speakers meeting at the same location as well as the result of sound
from a speaker meeting with sound reflected off the walls and ceilings. If the sound
arrives at a given location such that compressions meet rarefactions, then destructive
interference will occur resulting in a reduction in the loudness of the sound at that
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location. One means of reducing the severity of destructive interference is by the design
of walls, ceilings, and baffles that serve to absorb sound rather than reflect it. This will
be discussed in more detaillater in Lesson 3.
The destructive interference of sound waves can also be used advantageously in noise
reduction systems. Earphones have been produced that can be used by factory andconstruction workers to reduce the noise levels on their jobs. Such earphones capture
sound from the environment and use computer technology to produce a second sound
wave that one-half cycle out of phase. The combination of these two sound waves within
the headset will result in destructive interference and thus reduce a worker's exposure
to loud noise.
Musical Beats and Intervals
Interference of sound waves has widespread applications in the world of music. Musicseldom consists of sound waves of a single frequency played continuously. Few music
enthusiasts would be impressed by an orchestra that played music consisting of the
note with a pure tone played by all instruments in the orchestra. Hearing a sound wave
of 256 Hz (middle C) would become rather monotonous (both literally and figuratively).
Rather, instruments are known to produce overtones when played resulting in a sound
that consists of a multiple of frequencies. Such instruments are described as being rich
in tone color. And even the best choirs will earn their moneywhen two singers sing two
notes (i.e., produce two sound waves) that are anoctave apart.Music is a mixture of
sound waves that typically have whole number ratios between the frequencies
associated with their notes. In fact, the major distinction between music and noise isthat noise consists of a mixture of frequencies whose mathematical relationship to one
another is not readily discernible. On the other hand, music consists of a mixture of
frequencies that have aclear mathematical relationshipbetween them. While it may be
true that "one person's music is another person's noise" (e.g., your music might be
thought of by your parents as being noise), a physical analysis of musical sounds
reveals a mixture of sound waves that are mathematically related.
To demonstrate this nature of music, let's consider one of the simplest mixtures of two
different sound waves - two sound waves with a 2:1 frequency ratio. This combination
of waves is known as an octave. A simple sinusoidal plot of the wave pattern for twosuch waves is shown below. Note that the red wave has two times the frequency of the
blue wave. Also observe that the interference of these two waves produces a resultant
(in green) that has a periodic and repeating pattern. One might say that two sound
waves that have a clear whole number ratio between their frequencies interfere to
produce a wave with a regular and repeating pattern. The result is music.
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Another simple example of two sound waves with a clear mathematical relationship
between frequencies is shown below. Note that the red wave has three-halves the
frequency of the blue wave. In the music world, such waves are said to bea fifth
apartand represent a popular musical interval. Observe once more that the interference
of these two waves produces a resultant (in green) that has a periodic and repeating
pattern. It should be said again: two sound waves that have a clear whole number ratio
between their frequencies interfere to produce a wave with a regular and repeating
pattern; the result is music.
Finally, the diagram below illustrates the wave pattern produced by two dissonant or
displeasing sounds. The diagram shows two waves interfering, but this time there is
nosimplemathematical relationship between their frequencies (in computer terms, one
has a wavelength of 37 and the other has a wavelength 20 pixels). Observe (lookcarefully) that the pattern of the resultant is neither periodic nor repeating (at least not
in the short sample of time that is shown). The message is clear: if two sound waves
that have no simple mathematical relationship between their frequencies interfere to
produce a wave, the result will be an irregular and non-repeating pattern. This tends to
be displeasing to the ear.
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The beat frequencyrefers to the rate at which the volume is heard to be oscillating
from high to low volume. For example, if two complete cycles of high and low volumes
are heard every second, the beat frequency is 2 Hz. The beat frequency is always equal
to the difference in frequency of the two notes that interfere to produce the beats. So if
two sound waves with frequencies of 256 Hz and 254 Hz are played simultaneously, a
beat frequency of 2 Hz will be detected. A common physics demonstration involves
producing beats using two tuning forks with very similar frequencies. If a tine on one of
two identical tuning forks is wrapped with a rubber band, then that tuning forks
frequency will be lowered. If both tuning forks are vibrated together, then they produce
sounds with slightly different frequencies. These sounds will interfere to produce
detectable beats. The human ear is capable of detecting beats with frequencies of 7 Hz
and below.
A piano tuner frequently utilizes the phenomenon of beats to tune a piano string. She
will pluck the string and tap a tuning fork at the same time. If the two sound sources -
the piano string and the tuning fork - produce detectable beats then their frequencies
are not identical. She will then adjust the tension of the piano string and repeat the
process until the beats can no longer be heard. As the piano string becomes more in
tune with the tuning fork, the beat frequency will be reduced and approach 0 Hz. When
beats are no longer heard, the piano string is tuned to the tuning fork; that is, they play
the same frequency. The process allows a piano tuner to match the strings' frequency
to the frequency of a standardized set of tuning forks.
Suppose that there is a happy bug in the center of a circular water puddle. The bug is
periodically shaking its legs in order to produce disturbances that
travel through the water. If these disturbances originate at a
point, then they would travel outward from that point in all
directions. Since each disturbance is traveling in the same
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medium, they would all travel in every direction at the same speed. The pattern
produced by the bug's shakingwould be a series of concentric circles as shown in the
diagram at the right. These circles would reach the edges of the water puddle at the
same frequency. An observer at point A (the left edge of the puddle) would observe the
disturbances to strike the puddle's edge at the same frequency that would be observed
by an observer at point B (at the right edge of the puddle). In fact, the frequency at
which disturbances reach the edge of the puddle would be the same as the frequency
at which the bug produces the disturbances. If the bug produces disturbances at a
frequency of 2 per second, then each observer would observe them approaching at a
frequency of 2 per second.
Now suppose that our bug is moving to the right across the puddle of water and
producing disturbances at the same frequency of 2 disturbances
per second. Since the bug is moving towards the right, each
consecutive disturbance originates from a position that is closer
to observer B and farther from observer A. Subsequently, eachconsecutive disturbance has a shorter distance to travel before
reaching observer B and thus takes less time to reach observer B.
Thus, observer B observes that the frequency of arrival of the
disturbances is higher than the frequency at which disturbances
are produced. On the other hand, each consecutive disturbance has a further distance
to travel before reaching observer A. For this reason, observer A observes a frequency
of arrival that is less than the frequency at which the disturbances are produced. The
net effect of the motion of the bug (the source of waves) is that the observer towards
whom the bug is moving observes a frequency that is higher than 2
disturbances/second; and the observer away from whom the bug is moving observes a
frequency that is less than 2 disturbances/second. This effect is known as the Doppler
effect.
The Doppler effect is observed whenever the source of waves is moving with respect to
an observer. The Doppler effectcan be described as the effect produced by a moving
source of waves in which there is an apparent upward shift in frequency for observers
towards whom the source is approaching and an apparent downward shift in frequency
for observers from whom the source is receding. It is important to note that the effect
does not result because of an actual change in the frequency of the source. Using the
example above, the bug is still producing disturbances at a rate of 2 disturbances persecond; it just appears to the observer whom the bug is approaching that the
disturbances are being produced at a frequency greater than 2 disturbances/second.
The effect is only observed because the distance between observer B and the bug is
decreasing and the distance between observer A and the bug is increasing.
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The Doppler effect can be observed for any type of wave - water wave, sound wave,
light wave, etc. We are most familiar with the Doppler effect because of our
experiences with sound waves. Perhaps you recall an instance in which a police car or
emergency vehicle was traveling towards you on the highway. As the car approached
with its siren blasting, the pitch of the siren sound (a measure of the siren's frequency)
was high; and then suddenly after the car passed by, the pitch of the siren sound was
low. That was the Doppler effect - an apparent shift in frequency for a sound wave
produced by a moving source.
The Doppler effect is of intense interest to astronomers who use the information about
the shift in frequency of electromagnetic waves produced by moving stars in our galaxy
and beyond in order to derive information about those stars and galaxies. The belief
that the universe is expanding is based in part upon observations of electromagnetic
waves emitted by stars in distant galaxies. Furthermore, specific information about stars
within galaxies can be determined by application of the Doppler effect. Galaxies are
clusters of stars that typically rotate about some center of mass point. Electromagnetic
radiation emitted by such stars in a distant galaxy would appear to be shifted
downward in frequency (a red shift) if the star is rotating in its cluster in a direction that
is away from the Earth. On the other hand, there is an upward shift in frequency
(a blue shift) of such observed radiation if the star is rotating in a direction that is
towards the Earth.
As a wave travels through a medium, it will often reach the end of the medium and
encounter an obstacle or perhaps another medium through which it could travel.
Oneexampleof this has already been mentioned in Lesson 2. A sound wave is known to
reflect off canyon walls and other obstacles to produce an echo. A sound wave travelingthrough air within a canyon reflects off the canyon wall and returns to its original
source. What affect does reflection have upon a wave? Does reflection of a wave affect
the speed of the wave? Does reflection of a wave affect the wavelength and frequency
of the wave? Does reflection of a wave affect the amplitude of the wave? Or does
reflection affect other properties and characteristics of a wave's motion? The behavior
of a wave (or pulse) upon reaching the end of a medium is referred to as boundary
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behavior. When one medium ends, another medium begins; the interface of the two
media is referred to as the boundaryand the behavior of a wave at that boundary is
described as its boundary behavior. The questions that are listed above are the types of
questions we seek to answer when we investigate the boundary behavior of waves. the
behavior of waves traveling along a rope from a more dense medium to a less dense
medium (and vice versa) was discussed. The wave doesn't juststopwhen it reaches the
end of the medium. Rather, a wave will undergo certain behaviors when it encounters
the end of the medium. Specifically, there will be some reflection off the boundary and
some transmission into the new medium. But what if the wave is traveling in a two-
dimensional medium such as a water wave traveling through ocean water? Or what if
the wave is traveling in a three-dimensional medium such as a sound wave or a light
wave traveling through air? What types of behaviors can be expected of such two- and
three-dimensional waves?
The study of waves in two dimensions is often done using a
ripple tank. A ripple tank is a large glass-bottomed tank ofwater that is used to study the behavior of water waves. A
light typically shines upon the water from above and
illuminates a white sheet of paper placed directly below the
tank. A portion of light is absorbed by the water as it passes
through the tank. A crest of water will absorb more light than
a trough. So the bright spots represent wave troughs and the
dark spots represent wave crests. As the water waves move
through the ripple tank, the dark and bright spots move as
well. As the waves encounter obstacles in their path, their
behavior can be observed by watching the movement of the dark and bright spots on
the sheet of paper. Ripple tank demonstrations are commonly done in a Physics class in
order to discuss the principles underlying the reflection, refraction, and diffraction of
waves.
If a linear object attached to an oscillator bobs back and forth within the water, it
becomes a source of straightwaves. These straight waves have alternating crests and
troughs. As viewed on the sheet of paper below the tank, the crests are the dark lines
stretching across the paper and the troughs are the bright lines. These
waves will travel through the water until they encounter an obstacle -
such as the wall of the tank or an object placed within the water. Thediagram at the right depicts a series of straight waves approaching a
long barrier extending at an angle across the tank of water. The
direction that these wavefronts (straight-line crests) are traveling
through the water is represented by the blue arrow. The blue arrow is called a rayand
is drawn perpendicular to the wavefronts. Upon reaching the barrier placed within the
water, these waves bounce off the water and head in a different direction. The diagram
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below shows the reflected wavefronts and the reflected ray. Regardless of the angle at
which the wavefronts approach the barrier, one general law of reflection holds true: the
waves will always reflect in such a way that the angle at which they approach the
barrier equals the angle at which they reflect off the barrier. This is known as the law
of reflection. This law will be discussed in more detail inUnit 13 of The Physics
Classroom.
The discussion above pertains to the reflection of waves off of straight
surfaces. But what if the surface is curved, perhaps in the shape of a
parabola? What generalizations can be made for the reflection of water
waves off parabolic surfaces? Suppose that a rubber tube having the
shape of a parabola is placed within the water. The diagram at the
right depicts such a parabolic barrier in the ripple tank. Several
wavefronts are approaching the barrier; the ray is drawn for these wavefronts. Upon
reflection off the parabolic barrier, the water waves will change direction and head
towards a point. This is depicted in the diagram below. It is as though all the energy
being carried by the water waves is converged at a single point - the point is known asthe focal point. After passing through the focal point, the waves spread out through the
water. Reflection of waves off of curved surfaces will be discussed in more detail in Unit
13 of The Physics Classroom.
Reflection involves a change in direction of waves when they bounce off a
barrier.Refractionof waves involves a change in the direction of waves as they pass
from one medium to another. Refraction, or the bending of the path of the waves, is
accompanied by a change in speed and wavelength of the waves. InLesson 2,it was
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mentioned that the speed of a wave is dependent upon the properties of the medium
through which the waves travel. So if the medium (and its properties) is changed, the
speed of the waves is changed. The most significant property of water that would affect
the speed of waves traveling on its surface is the depth of the water. Water waves
travel fastest when the medium is the deepest. Thus, if water waves are passing from
deep water into shallow water, they will slow down. And as mentioned inthe previous
section of Lesson 3,this decrease in speed will also be accompanied by a decrease in
wavelength. So as water waves are transmitted from deep water into shallow water,
the speed decreases, the wavelength decreases, and the direction
changes.
This boundary behavior of water waves can be observed in a ripple
tank if the tank is partitioned into a deep and a shallow section. If a
pane of glass is placed in the bottom of the tank, one part of the tank
will be deep and the other part of the tank will be shallow. Waves
traveling from the deep end to the shallow end can be seen to refract (i.e., bend),decrease wavelength (the wavefronts get closer together), and slow down (they take a
longer time to travel the same distance). When traveling from deep water to shallow
water, the waves are seen to bend in such a manner that they seem to be traveling
more perpendicular to the surface. If traveling from shallow water to deep water, the
waves bend in the opposite direction. The refraction of light waves will be discussed in
more detail ina later unit of The Physics Classroom.
Reflection involves a change in direction of waves when they bounce off a
barrier;refractionof waves involves a change in the direction of waves
as they pass from one medium to another; and diffractioninvolves a
change in direction of waves as they pass through an opening or
around a barrier in their path. Water waves have the ability to travel
around corners, around obstacles and through openings. This ability is
most obvious for water waves with longer wavelengths. Diffraction can
be demonstrated by placing small barriers and obstacles in a ripple
tank and observing the path of the water waves as they encounter the obstacles. The
waves are seen to pass around the barrier into the regions behind it; subsequently the
water behind the barrier is disturbed. The amount of diffraction (the sharpness of thebending) increases with increasing wavelength and decreases with decreasing
wavelength. In fact, when the wavelength of the waves is smaller than the obstacle, no
noticeable diffraction occurs.
Diffraction of water waves is observed in a harbor as waves bend around small boats
and are found to disturb the water behind them. The same waves however are unable
to diffract around larger boats since their wavelength is smaller than the boat.
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Diffraction of sound waves is commonly observed; we notice sound diffracting around
corners, allowing us to hear others who are speaking to us from adjacent rooms. Many
forest-dwelling birds take advantage of the diffractive ability of long-wavelength sound
waves. Owls for instance are able to communicate across long distances due to the fact
that their long-wavelength hootsare able to diffract around forest trees and carry
farther than the short-wavelength tweetsof songbirds. Diffraction is observed of light
waves but only when the waves encounter obstacles with extremely small wavelengths
(such as particles suspended in our atmosphere). Diffraction ofsound wavesand
oflight waveswill be discussed in a later unit ofThe Physics Classroom Tutorial.
Reflection, refraction and diffraction are all boundary behaviors of waves associated
with the bending of the path of a wave. The bending of the path is an observable
behavior when the medium is a two- or three-dimensional medium. Reflection occurs
when there is a bouncing off of a barrier. Reflection of waves off straight barriersfollows the law of reflection. Reflection of waves off parabolic barriers results in the
convergence of the waves at a focal point. Refraction is the change in direction of
waves that occurs when waves travel from one medium to another. Refraction is always
accompanied by a wavelength and speed change. Diffraction is the bending of waves
around obstacles and openings. The amount of diffraction increases with increasing
wavelength.
The Bernoulli effect, or the Bernoulli principle or Bernoulli's law, is a statement of relationship
between flow speed and pressure in a fluid system; in essence, when the speed of horizontal flow
through a fluid increases, the pressure decreases. This effect, and the principle which states this
formally, was discovered by the renowned mathematician Daniel Bernoulli, who first published itsformulation in 1738. Since the word "fluid" inphysicsrefers to the behavior of both liquids and
gasses, such as air, the Bernoulli effect can be observed in both hydrodynamic, or fluid, systems as
well as aerodynamic, or gaseous, systems.
A common example used to explain the Bernoulli effect is the flow of fluid through a pipe. If the fluid
is moving uniformly through the pipe, then the only forces acting on the fluid are its own weight and
the pressure of the fluid itself. Now, if the pipe narrows, the fluid must speed up, because the same
amount of fluid is traveling through a smaller space. However, if the fluid is moving uniformly, and
the weight has not changed, then the only way in which the fluid will move faster is if the pressure
behind the fluid is greater than the pressure in front. Thus, the pressure must decrease as the speed
increases.
As has beenpreviously mentionedin this unit, a sound wave is created as a result of a
vibrating object. The vibrating object is the source of the disturbance that moves
through the medium. The vibrating object that creates the disturbance could be the
vocal cords of a person, the vibrating string and soundboard of a guitar or violin, the
vibrating tines of a tuning fork, or the vibrating diaphragm of a radio speaker. Any
object that vibrates will create a sound. The sound could be musical or it could be noisy;
but regardless of its quality, the sound wave is created by a vibrating object.
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Nearly all objects, when hit or struck or plucked or strummed or somehow disturbed,
will vibrate. If you drop a meter stick or pencil on the floor, it will begin to vibrate. If
you pluck a guitar string, it will begin to vibrate. If you blow over the top of a pop
bottle, the air inside will vibrate. When each of these objects vibrates, they tend to
vibrate at a particular frequency or a set of frequencies. The frequency or frequencies
at which an object tends to vibrate with when hit, struck, plucked, strummed or
somehow disturbed is known as the natural frequencyof the object. If the
amplitudes of the vibrations are large enough and if natural frequency is within
thehuman frequency range,then the vibrating object will produce sound waves that
are audible.
All objects have a natural frequency or set of frequencies at which they vibrate. The
quality or timbreof the sound produced by a vibrating object is dependent upon the
natural frequencies of the sound waves produced by the objects. Some objects tend to
vibrate at a single frequency and they are often said to produce a pure tone. A flute
tends to vibrate at a single frequency, producing a very pure tone. Other objects vibrateand produce more complex waves with a set of frequencies that have awhole number
mathematical relationshipbetween them; these are said to produce a rich sound. A
tuba tends to vibrate at a set of frequencies that are mathematically related by whole
number ratios; it produces a rich tone. Still other objects will vibrate at a set of multiple
frequencies that have no simple mathematical relationship between them. These
objects are not musical at all and the sounds that they create could be described
asnoise.When a meter stick or pencil is dropped on the floor, it vibrates with a number
of frequencies, producing a complex sound wave that is clanky and noisy.
The actual frequency at which an object will vibrate at is determined by a variety of
factors. Each of these factors will either affect the wavelength or the speed of the
object. Since
frequency = speed/wavelength
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an alteration in either speed or wavelength will result in an alteration of the natural
frequency. The role of a musician is to control these variables in order to produce a
given frequency from the instrument that is being played. Consider a guitar as an
example. There are six strings, each having a different linear density (the wider strings
are more dense on a per meter basis), a different tension (which is controllable by the
guitarist), and a different length (also controllable by the guitarist). The speed at which
waves move through the strings isdependent upon the properties of the medium- in
this case the tightness (tension) of the string and the linear density of the strings.
Changes in these properties would affect the natural frequency of the particular string.
The vibrating portion of a particular string can be shortenedby pressing the string
against one of the frets on the neck of the guitar. This modification in the length of the
string would affect the wavelength of the wave and in turn the natural frequency at
which a particular string vibrates at. Controlling the speed and the wavelength in this
manner allows a guitarist to control the natural frequencies of the vibrating object (a
string) and thus produce the intended musical sounds. The same principles can beapplied to any string instrument - whether it is the harp, harpsichord, violin or guitar.
As another example, consider the trombone with its long cylindrical tube that is bent
upon itself twice and ends in a flared end. The trombone is an example of a wind
instrument. The tubeof any wind instrument acts as a container for a vibrating air
column. The air inside the tube will be set into vibration by a vibrating reed or the
vibrations of a musician's lips against a mouthpiece. While the speed of sound waves
within the air column is not alterable by the musician (they can only be altered
bychanges in room temperature), the length of the air column is. For a trombone, the
length is altered by pushing the tube outward away from the mouthpiece to lengthen it
or pulling it in to shorten it. This causes the length of the air column to be changed,
and subsequently changes the wavelength of the waves it produces. And of course, a
change in wavelength will result in a change in the frequency. So the natural frequency
of a wind instrument such as the trombone is dependent upon the length of the air
column of the instrument. The same principles can be applied to any similar instrument
(tuba, flute, wind chime, organ pipe, clarinet, or pop bottle) whose sound is produced
by vibrations of air within a tube.
There were a variety of classroom demonstrations (some of which are
fun
top related