Sound wave
Sound and music are parts of our everyday sensory experience. Just as humans have eyes for the
detection of light and color, so we are equipped with ears for the detection of sound. We seldom take
the time to ponder the characteristics and behaviors of sound and the mechanisms by which sounds are
produced, propagated, and detected. The basis for an understanding of sound, music and hearing is the
physics of waves. Sound is a wave that is created by vibrating objects and propagated through a medium
from one location to another. In this unit, we will investigate the nature, properties and behaviors of
sound waves and apply basic wave principles towards an understanding of music.
As discussed in the previous unit of The Physics Classroom Tutorial, a wave can be described as a
disturbance that travels through a medium, transporting energy from one location to another location.
The medium is simply the material through which the disturbance is moving; it can be thought of as a
series of interacting particles. The example of a slinky wave is often used to illustrate the nature of a
wave. A disturbance is typically created within the slinky by the back and forth movement of the first
coil of the slinky. The first coil becomes disturbed and begins to push or pull on the second coil. This
push or pull on the second coil will displace the second coil from its equilibrium position. As the second
coil becomes displaced, it begins to push or pull on the third coil; the push or pull on the third coil
displaces it from its equilibrium position. As the third coil becomes displaced, it begins to push or pull on
the fourth coil. This process continues in consecutive fashion, with each individual particle acting to
displace the adjacent particle. Subsequently the disturbance travels through the slinky. As the
disturbance moves from coil to coil, the energy that was originally introduced into the first coil is
transported along the medium from one location to another.
A sound wave is similar in nature to a slinky wave for a variety of reasons. First, there is a medium that
carries the disturbance from one location to another. Typically, this medium is air, though it could be
any material such as water or steel. The medium is simply a series of interconnected and interacting
particles. Second, there is an original source of the wave, some vibrating object capable of disturbing the
first particle of the medium. The disturbance could be created by the vibrating 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. Third, the sound wave is transported from one location to
another by means of particle-to-particle interaction. If the sound wave is moving through air, then as
one air particle is displaced from its equilibrium position, it exerts a push or pull on its nearest
neighbors, causing them to be displaced from their equilibrium position. This particle interaction
continues throughout the entire medium, with each particle interacting and causing a disturbance of its
nearest neighbors. Since a sound wave is a disturbance that is transported through a medium via the
mechanism of particle-to-particle interaction, a sound wave is characterized as a mechanical wave.
Production and Propagation of Sound Waves
The creation and propagation of sound waves are often demonstrated in class through the use of a
tuning fork. A tuning fork is a metal object consisting of two tines capable of vibrating if struck by a
rubber hammer or mallet. As the tines of the tuning forks vibrate back and forth, they begin to disturb
surrounding air molecules. These disturbances are passed on to adjacent air molecules by the
mechanism of particle interaction. The motion of the disturbance, originating at the tines of the tuning
fork and traveling through the medium (in this case, air) is what is referred to as a sound wave. The
generation and propagation of a sound wave is demonstrated in the animation below.
Many Physics demonstration tuning forks are mounted on a sound box. In such instances, the vibrating
tuning fork, being connected to the sound box, sets the sound box into vibrational motion. In turn, the
sound box, being connected to the air inside of it, sets the air inside of the sound box into vibrational
motion. As the tines of the tuning fork, the structure of the sound box, and the air inside of the sound
box begin vibrating at the same frequency, a louder sound is produced. In fact, the more particles that
can be made to vibrate, the louder or more amplified the sound. This concept is often demonstrated by
the placement of a vibrating tuning fork against the glass panel of an overhead projector or on the
wooden door of a cabinet. The vibrating tuning fork sets the glass panel or wood door into vibrational
motion and results in an amplified sound.
We know that a tuning fork is vibrating because we hear the sound that is produced by its vibration.
Nonetheless, we do not actually visibly detect any vibrations of the tines. This is because the tines are
vibrating at a very high frequency. If the tuning fork that is being used corresponds to middle C on the
piano keyboard, then the tines are vibrating at a frequency of 256 Hertz; that is, 256 vibrations per
second. We are unable to visibly detect vibrations of such high frequency. A common physics
demonstration involves slowing down the vibrations by through the use of a strobe light. If the strobe
light puts out a flash of light at a frequency of 512 Hz (two times the frequency of the tuning fork), then
the tuning fork can be observed to be moving in a back and forth motion. With the room darkened, the
strobe would allow us to view the position of the tines two times during their vibrational cycle. Thus we
would see the tines when they are displaced far to the left and again when they are displaced far to the
right. This would be convincing proof that the tines of the tuning fork are indeed vibrating to produce
sound.
In a previous unit of The Physics Classroom Tutorial, a distinction was made between two categories of
waves: mechanical waves and electromagnetic waves. Electromagnetic waves are waves that have an
electric and magnetic nature and are capable of traveling through a vacuum. Electromagnetic waves do
not require a medium in order to transport their energy. Mechanical waves are waves that require a
medium in order to transport their energy from one location to another. Because mechanical waves rely
on particle interaction in order to transport their energy, they cannot travel through regions of space
that are void of particles. That is, mechanical waves cannot travel through a vacuum. This feature of
mechanical waves is often demonstrated in a Physics class. A ringing bell is placed in a jar and air inside
the jar is evacuated. Once air is removed from the jar, the sound of the ringing bell can no longer be
heard. The clapper is seen striking the bell; but the sound that it produces cannot be heard because
there are no particles inside of the jar to transport the disturbance through the vacuum. Sound is a
mechanical wave and cannot travel through a vacuum.
phase difference etc
tch and Frequency
Intensity and the Decibel Scale
The Speed of Sound
The Human Ear
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. The frequency of a
wave refers 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 1000 longitudinal vibrations in 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.
And of course the frequency at which each particle vibrates is the same as the frequency of the original
source of the sound 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 signal to 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 a pressure 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
the detector 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.
Since a pressure-time plot shows the fluctuations in pressure over time, the period of 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.
Frequency, Pitch and Human Perception
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
discussed later 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
infrasound and 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 as
high 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 pitch of a sound. A high pitch sound
corresponds to a high frequency sound wave and a low pitch sound 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 the interference and
superposition of the two sound waves. Certain sound waves when played (and heard) simultaneously
will produce a particularly pleasant sensation when heard, are said to be consonant. Such sound waves
form the basis of intervals in music. For example, any two sounds whose frequencies make a 2:1 ratio
are said to be separated by an octave and 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
Examples
Octave
2:1
512 Hz and 256 Hz
Third
5:4
320 Hz and 256 Hz
Fourth
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. In the next part of Lesson 2, we will investigate
the ability of the ear to perceive the intensity of a sound wave.
sound wave and equation
super position of wave
interference
Interference and Beats
Interference and Beats
The Doppler Effect and Shock Waves
Boundary Behavior
Reflection, Refraction, and Diffraction
Wave interference is the phenomenon that occurs when two waves meet while traveling 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 in a previous unit of
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.
standing wave
Standing Wave Patterns
Natural Frequency
Forced Vibration
Standing Wave Patterns
Fundamental Frequency and Harmonics
As mentioned earlier, all objects have a frequency or set of frequencies with which they naturally vibrate
when struck, plucked, strummed or somehow disturbed. Each of the natural frequencies at which an
object vibrates is associated with a standing wave pattern. When an object is forced into resonance
vibrations at one of its natural frequencies, it vibrates in a manner such that a standing wave is formed
within the object. The topic of standing wave patterns was introduced in Unit 10 of The Physics
Classroom. In that unit, a standing wave pattern was described as a vibrational pattern created within a
medium when the vibrational frequency of a source causes reflected waves from one end of the
medium to interfere with incident waves from the source, The result of the interference is that specific
points along the medium appear to be standing still while other points vibrated back and forth. Such
patterns are only created within the medium at specific frequencies of vibration. These frequencies are
known as harmonic frequencies or merely harmonics. At any frequency other than a harmonic
frequency, the interference of reflected and incident waves results in a disturbance of the medium that
is irregular and non-repeating.
travelling wave
transvers and longitudinal wave
resonance beat