Introduction to Waves
The Concept of Wave
Explain the concept of a wave
A wave is a disturbance that travels through a medium from one location to another location.
Consider a slinky wave as an example of a wave. When the slinky is stretched from end to end and is held at rest, it assumes a natural position known as the equilibrium or rest position.
The coils of the slinky naturally assume this position, spaced equally far apart. To introduce a wave into the slinky, the first particle is displaced or moved from its equilibrium or rest position. The particle might be moved upwards or downwards, forwards or backwards; but once moved, it is returned to its original equilibrium or rest position.
The act of moving the first coil of the slinky in a given direction and then returning it to its equilibrium position creates a disturbance in the slinky. We can then observe this disturbance moving through the slinky from one end to the other. If the first coil of the slinky is given a single back-and-forth vibration, then we call the observed motion of the disturbance through the slinky a slinky pulse.
A pulse is a single disturbance moving through a medium from one location to another location.
However,
if the first coil of the slinky is continuously and periodically
vibrated in a back-and-forth manner, we would observe a repeating
disturbance moving within the slinky that endures over some prolonged
period of time. The repeating and periodic disturbance that moves
through a medium from one location to another is referred to as a wave.
if the first coil of the slinky is continuously and periodically
vibrated in a back-and-forth manner, we would observe a repeating
disturbance moving within the slinky that endures over some prolonged
period of time. The repeating and periodic disturbance that moves
through a medium from one location to another is referred to as a wave.
A medium is a substance or material that carries the wave.
You have perhaps heard of the phrase news media.
The news media refers to the various institutions (newspaper offices,
television stations, radio stations, etc.) within our society that carry
the news from one location to another. The news moves through the media.
The news media refers to the various institutions (newspaper offices,
television stations, radio stations, etc.) within our society that carry
the news from one location to another. The news moves through the media.
The
wave medium is not the wave and it doesn’t make the wave; it merely
carries or transports the wave from its source to other locations.
wave medium is not the wave and it doesn’t make the wave; it merely
carries or transports the wave from its source to other locations.
In
the case of our slinky wave, the medium through that the wave travels
is the slinky coils. In the case of a water wave in the ocean, the
medium through which the wave travels is the ocean water. In the case of
a sound wave moving from the church choir to the pews, the medium
through which the sound wave travels is the air in the room.
the case of our slinky wave, the medium through that the wave travels
is the slinky coils. In the case of a water wave in the ocean, the
medium through which the wave travels is the ocean water. In the case of
a sound wave moving from the church choir to the pews, the medium
through which the sound wave travels is the air in the room.
The Terms Wave Length, Frequency and Velocity of a Wave
Explain the terms wave length, frequency and velocity of a wave
Consider the transverse wave below:
- A transverse
wave is a wave in which the particles of the medium are displaced in a
direction perpendicular to the direction of energy transport. - The crest
of a wave is the point on the medium that exhibits the maximum amount
of positive or upward displacement from the rest position. - The trough
of a wave is the point on the medium that exhibits the maximum amount
of negative or downward displacement from the rest position. - The amplitude
of 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
distance from rest to crest. Similarly, the amplitude can be measured from the rest position to the trough position. - The wavelength
of 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. - A longitudinal
wave is 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. - A compression is 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 rarefaction
is 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. - The frequency, (f)
of a wave refers to how often the particles of the medium vibrate when a
wave passes through the medium. Given this definition, it is reasonable
that the quantity frequency would have units of cycles/second, waves/second, vibrations/second, or something/second. Another unit for frequency is the Hertz
(abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. If a coil
of slinky makes 2 vibrational cycles in one second, then the frequency
is 2 Hz. - Period, (T) refers to the time that it takes to do something. When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period. The period
of a wave is the time for a particle on a medium to make one complete
vibrational cycle. Period, being a time, is measured in units of time
such as seconds, hours, days or years. The period of orbit for the Earth
around the Sun is approximately 365 days; it takes 365 days for the
Earth to complete a cycle. - The speed of an
object refers to how fast an object is moving and is usually expressed
as the distance traveled per time of travel. In the case of a wave, the
speed is the distance traveled by a given point on the wave (such as a
crest) in a given interval of time.The SI unit of speed is m/s.
Wave equation
The wave equation shows the relationship between speed, wavelength and frequency of a wave.
The
diagrams below show several “snapshots” of the production of a wave
within a rope. The motion of the disturbance along the medium after
every one-fourth of a period is depicted. Observe that in the time it
takes from the first to the last snapshot, the hand has made one
complete back-and-forth motion.
diagrams below show several “snapshots” of the production of a wave
within a rope. The motion of the disturbance along the medium after
every one-fourth of a period is depicted. Observe that in the time it
takes from the first to the last snapshot, the hand has made one
complete back-and-forth motion.
A
period has elapsed. Observe that during this same amount of time, the
leading edge of the disturbance has moved a distance equal to one
complete wavelength. So in a time of one period, the wave has moved a
distance of one wavelength. Combining this information with the equation
for speed (speed = distance/time), it can be said that the speed of a
wave is also the wavelength/period.
period has elapsed. Observe that during this same amount of time, the
leading edge of the disturbance has moved a distance equal to one
complete wavelength. So in a time of one period, the wave has moved a
distance of one wavelength. Combining this information with the equation
for speed (speed = distance/time), it can be said that the speed of a
wave is also the wavelength/period.
Since
the period is the reciprocal of the frequency, the expression 1/f can
be substituted into the above equation for period. Rearranging the
equation yields a new equation of the form:
the period is the reciprocal of the frequency, the expression 1/f can
be substituted into the above equation for period. Rearranging the
equation yields a new equation of the form:
Speed = Wavelength • Frequency.The above equation is known as the wave equation. It states the mathematical relationship between the speed (v) of a wave and its wavelength (λ) and frequency (f). Using the symbols v, λ, and f, the equation can be rewritten asv = f • λ
Types of Waves
Identify types of waves
Previously
we classified the waves by considering the movement of the particles.
And now you’re going to find out the 2 types of waves according to the
media of propagation.
we classified the waves by considering the movement of the particles.
And now you’re going to find out the 2 types of waves according to the
media of propagation.
- Mechanical Waves
- Electromagnetic Waves
Mechanical Waves
Mechanical
waves are also called elastic waves as their propagation depends on the
elastic properties of the medium through which the waves pass
waves are also called elastic waves as their propagation depends on the
elastic properties of the medium through which the waves pass
Mechanical
waves are divided into three categories: Transverse waves, longitudinal
waves, and surface waves. In transverse waves, the medium moves
perpendicular to the wave direction, and in longitudinal waves, the
medium moves parallel to the wave direction.
waves are divided into three categories: Transverse waves, longitudinal
waves, and surface waves. In transverse waves, the medium moves
perpendicular to the wave direction, and in longitudinal waves, the
medium moves parallel to the wave direction.
In
surface waves, both transverse and longitudinal waves mix in a single
medium. In very simple words, an electronic wave is that which travels
in a vacuum, and a mechanical wave is that which needs some medium for
traveling.
surface waves, both transverse and longitudinal waves mix in a single
medium. In very simple words, an electronic wave is that which travels
in a vacuum, and a mechanical wave is that which needs some medium for
traveling.
Examples of mechanical waves are Sound waves, Water waves , Ocean waves, Earth quake waves, Seismic waves
Electromagnetic Waves
Electromagnetic
waves are waves that have no medium to travel whereas mechanical waves
need a medium for its transmission. Examples of electromagnetic waves
include light and radio signals.
waves are waves that have no medium to travel whereas mechanical waves
need a medium for its transmission. Examples of electromagnetic waves
include light and radio signals.
The following are the differences between mechanical and electromagnetic waves.
- Electromagnetic waves travel in a vacuum whereas mechanical waves do not.
- The mechanical waves need a medium like water, air, or anything for it to travel.
- While an electromagnetic wave is called just a disturbance, a mechanical wave is considered a periodic disturbance.
Behaviour of Waves
Reflection, Refraction, Diffraction and Interference of Waves
Explain Reflection, refraction, diffraction and interference of waves
All waves behave in certain characteristic ways. They can undergo:
- Reflection
- Refraction
- Diffraction
- Interference
These
basic properties define the behaviour of a wave – anything that
reflects, refracts, diffracts and interferes is labelled a wave.
basic properties define the behaviour of a wave – anything that
reflects, refracts, diffracts and interferes is labelled a wave.
Reflection
Reflection
is the change in direction of a wavefront at an interface between two
different media so that the wavefront returns into the medium from which
it originated. Common examples include the reflection of light, sound
and water waves.
is the change in direction of a wavefront at an interface between two
different media so that the wavefront returns into the medium from which
it originated. Common examples include the reflection of light, sound
and water waves.
The law of reflection
If
the reflecting surface is very smooth, the reflection of light that
occurs is called specular or regular reflection. The laws of reflection
are as follows:
the reflecting surface is very smooth, the reflection of light that
occurs is called specular or regular reflection. The laws of reflection
are as follows:
- The
incident ray, the reflected ray and the normal to the reflection
surface at the point of the incidence lie in the same plane. - The angle which the incident ray makes with the normal is equal to the angle which the reflected ray makes to the same normal.
- The reflected ray and the incident ray are on the opposite sides of the normal.
Characteristics of Reflection of waves:
- It obeys the Law of Reflection.
- The wavelength, λ of the reflected wave is the same as that of the incident waves.
- The frequency,fof the reflected waves is the same as that of the incident waves.
- Therefore the speed, v of the reflected waves is the same as that of the incident waves.
Types of reflection:
- Specular: Smooth surfaces direct reflected light at opposite angle.
- Diffused: Rough surfaces scatter light in all directions.
- Spread: Some surfaces have a combination texture and smooth surface (varnish overcoat on paper, white label on white bottle).
Ripple Tank
A ripple tank
is a shallow glass tank of water used in schools and colleges to
demonstrate the basic properties of waves. It is a specialized form of a
wave tank. The ripple tank is usually illuminated from above, so that
the light shines through the water.
is a shallow glass tank of water used in schools and colleges to
demonstrate the basic properties of waves. It is a specialized form of a
wave tank. The ripple tank is usually illuminated from above, so that
the light shines through the water.
Some
small ripple tanks fit onto the top of an overhead projector, i.e. they
are illuminated from below. The ripples on the water show up as shadows
on the screen underneath the tank. All the basic properties of waves,
including reflection, refraction, interference and diffraction, can be
demonstrated.
small ripple tanks fit onto the top of an overhead projector, i.e. they
are illuminated from below. The ripples on the water show up as shadows
on the screen underneath the tank. All the basic properties of waves,
including reflection, refraction, interference and diffraction, can be
demonstrated.
Ripples
may be generated by a piece of wood that is suspended above the tank on
elastic bands so that it is just touching the surface. Screwed to wood
is a motor that has an off centre weight attached to the axle. As the
axle rotates the motor wobbles, shaking the wood and generating ripples.
may be generated by a piece of wood that is suspended above the tank on
elastic bands so that it is just touching the surface. Screwed to wood
is a motor that has an off centre weight attached to the axle. As the
axle rotates the motor wobbles, shaking the wood and generating ripples.
Refraction
Refraction is the change in direction of propagation of a wave due to a change in its transmission medium.
The
phenomenon is explained by the conservation of energy and conservation
of momentum. Due to change of medium, the phase velocity of the wave is
changed but its frequency remains constant. This is most commonly
observed when a wave passes from one medium to another at any angle
other than 0° from the normal.
phenomenon is explained by the conservation of energy and conservation
of momentum. Due to change of medium, the phase velocity of the wave is
changed but its frequency remains constant. This is most commonly
observed when a wave passes from one medium to another at any angle
other than 0° from the normal.
Refraction
of light is the most commonly observed phenomenon, but any type of wave
can refract when it interacts with a medium, for example when sound
waves pass from one medium into another or when water waves move into
water of a different depth.
of light is the most commonly observed phenomenon, but any type of wave
can refract when it interacts with a medium, for example when sound
waves pass from one medium into another or when water waves move into
water of a different depth.
Snell’s law
Refraction
is described by Snell’s law, which states that: “For a given pair of
media and a wave with a single frequency, the ratio of the sines of the
angle of incidence θ1 and angle of refraction θ2 is equivalent to the ratio of phase velocities (v1 / v2) in the two media, or equivalently, to the opposite ratio of the indices of refraction (n2 / n1)”
is described by Snell’s law, which states that: “For a given pair of
media and a wave with a single frequency, the ratio of the sines of the
angle of incidence θ1 and angle of refraction θ2 is equivalent to the ratio of phase velocities (v1 / v2) in the two media, or equivalently, to the opposite ratio of the indices of refraction (n2 / n1)”
The refractive index or index of refraction n
of an optical medium is a dimensionless number that describes how
light, or any other radiation, propagates through that medium.
of an optical medium is a dimensionless number that describes how
light, or any other radiation, propagates through that medium.
Refraction of a light ray.
The
refractive index determines how much light is bent, or refracted, when
entering a material. This is the historically first use of refractive
indices and is described by Snell’s law of refraction, n1 sin θ1 = n2 sin θ2, where θ1 and θ2
are the angles of incidence and refraction, respectively, of a ray
crossing the interface between two media with refractive indices n1 and n2.
refractive index determines how much light is bent, or refracted, when
entering a material. This is the historically first use of refractive
indices and is described by Snell’s law of refraction, n1 sin θ1 = n2 sin θ2, where θ1 and θ2
are the angles of incidence and refraction, respectively, of a ray
crossing the interface between two media with refractive indices n1 and n2.
The
refractive indices also determine the amount of light that is reflected
when reaching the interface, as well as the critical angle for total
internal reflection and Brewster’s angle.
refractive indices also determine the amount of light that is reflected
when reaching the interface, as well as the critical angle for total
internal reflection and Brewster’s angle.
Interference
Interference is a phenomenon in which two waves superpose to form a resultant wave of greater or lower amplitude.
Interference
usually refers to the interaction of waves that are correlated or
coherent with each other, either because they come from the same source
or because they have the same or nearly the same frequency.
usually refers to the interaction of waves that are correlated or
coherent with each other, either because they come from the same source
or because they have the same or nearly the same frequency.
Interference
effects can be observed with all types of waves, for example, light,
radio, acoustic, surface water waves or matter waves.
effects can be observed with all types of waves, for example, light,
radio, acoustic, surface water waves or matter waves.
Constructive Interference
Constructive interference
is a type of interference that occurs at any location along the medium
where the two interfering waves have a displacement in the same
direction.
is a type of interference that occurs at any location along the medium
where the two interfering waves have a displacement in the same
direction.
In
this case, both waves have an upward displacement; consequently, the
medium has an upward displacement that is greater than the displacement
of the two interfering pulses. Constructive interference is observed at
any location where the two interfering waves are displaced upward. But
it is also observed when both interfering waves are displaced downward.
this case, both waves have an upward displacement; consequently, the
medium has an upward displacement that is greater than the displacement
of the two interfering pulses. Constructive interference is observed at
any location where the two interfering waves are displaced upward. But
it is also observed when both interfering waves are displaced downward.
This is shown in the diagram below for two downward displaced pulses.
-In
this case, a sine pulse with a maximum displacement of -1 unit
(negative means a downward displacement) interferes with a sine pulse
with a maximum displacement of -1 unit. These two pulses are drawn in
red and blue. The resulting shape of the medium is a sine pulse with a
maximum displacement of -2 units. <!– [if
!supportLineBreakNewLine]–> <!–[endif]–>
this case, a sine pulse with a maximum displacement of -1 unit
(negative means a downward displacement) interferes with a sine pulse
with a maximum displacement of -1 unit. These two pulses are drawn in
red and blue. The resulting shape of the medium is a sine pulse with a
maximum displacement of -2 units. <!– [if
!supportLineBreakNewLine]–> <!–[endif]–>
Destructive Interference
Destructive interference
is a type of interference that occurs at any location along the medium
where the two interfering waves have a displacement in the opposite
direction.
is a type of interference that occurs at any location along the medium
where the two interfering waves have a displacement in the opposite
direction.
For
instance, when a sine pulse with a maximum displacement of +1 unit
meets a sine pulse with a maximum displacement of -1 unit, destructive
interference occurs.
instance, when a sine pulse with a maximum displacement of +1 unit
meets a sine pulse with a maximum displacement of -1 unit, destructive
interference occurs.
Diffraction
Diffraction refers to a change in direction of waves as they pass through an opening or around a barrier in their path.
In
classical physics, the diffraction phenomenon is described as the
interference of waves according to the Huygens–Fresnel principle. These
characteristic behaviors are exhibited when a wave encounters an
obstacle or a slit that is comparable in size to its wavelength. Similar
effects occur when a light wave travels through a medium with a varying
refractive index, or when a sound wave travels through a medium with
varying acoustic impedance.
classical physics, the diffraction phenomenon is described as the
interference of waves according to the Huygens–Fresnel principle. These
characteristic behaviors are exhibited when a wave encounters an
obstacle or a slit that is comparable in size to its wavelength. Similar
effects occur when a light wave travels through a medium with a varying
refractive index, or when a sound wave travels through a medium with
varying acoustic impedance.
Diffraction
occurs with all waves, including sound waves, water waves, and
electromagnetic waves such as visible light, X-rays and radio waves.
Diffraction arises because of the way in which waves propagate; this is
described by the Huygens–Fresnel principle and the principle of
superposition of waves.
occurs with all waves, including sound waves, water waves, and
electromagnetic waves such as visible light, X-rays and radio waves.
Diffraction arises because of the way in which waves propagate; this is
described by the Huygens–Fresnel principle and the principle of
superposition of waves.
The
propagation of a wave can be visualized by considering every particle
of the transmitted medium on a wavefront as a point source for a
secondary spherical wave. The wave displacement at any subsequent point
is the sum of these secondary waves.
propagation of a wave can be visualized by considering every particle
of the transmitted medium on a wavefront as a point source for a
secondary spherical wave. The wave displacement at any subsequent point
is the sum of these secondary waves.
When
waves are put together, their sum is determined by the relative phases
as well as the amplitudes of the individual waves so that the summed
amplitude of the waves can have any value between zero and the sum of
the individual amplitudes.
waves are put together, their sum is determined by the relative phases
as well as the amplitudes of the individual waves so that the summed
amplitude of the waves can have any value between zero and the sum of
the individual amplitudes.
A
long slit of infinitesimal width which is illuminated by light
diffracts the light into a series of circular waves and the wavefront
which emerges from the slit is a cylindrical wave of uniform intensity.A
slit which is wider than a wavelength produces interference effects in
the space downstream of the slit. These can be explained by assuming
that the slit behaves as though it has a large number of point sources
spaced evenly across the width of the slit
long slit of infinitesimal width which is illuminated by light
diffracts the light into a series of circular waves and the wavefront
which emerges from the slit is a cylindrical wave of uniform intensity.A
slit which is wider than a wavelength produces interference effects in
the space downstream of the slit. These can be explained by assuming
that the slit behaves as though it has a large number of point sources
spaced evenly across the width of the slit
Diffraction
of water waves is observed in a harbor as waves bend around small boats
and are found to disturb the water behind them. 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.
of water waves is observed in a harbor as waves bend around small boats
and are found to disturb the water behind them. 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.
Diffraction
is observed of light waves but only when the waves encounter obstacles
with extremely small wavelengths (such as particles suspended in our
atmosphere).
is observed of light waves but only when the waves encounter obstacles
with extremely small wavelengths (such as particles suspended in our
atmosphere).
The Application of Reflection, Refraction, Diffraction and Interference of Waves in Daily Life
Mention the application of reflection, refraction, diffraction and interference of waves in daily life
Application of reflection of waves
- The
phenomenon of the reflection of sound is used to determine the distance
between the two objects, for example depth of seabed, depth of cave or
width of a valley. The type of sound used must be ultrasound. - Sonar
(Sound Navigation and Ranging). Sonar is used to detect underwater
objects (corals / fishes) or to determine the depth of the water by
means of an echo. Sonar equipment emits a high frequency sound signal
which is reflected by the object in the water. The reflected sound wave
is received by the sonar receiver. The time taken for the echo to return
is used to determine the distance of the object below the water
surface. Sonar waves of high frequency is used because itpossessesmore
energy, high penetration power and can travel further through water. - Reflection of light waves is used in the design of mirrors.
- Detection of cracks in metals.
- Determination of frequency of A.C’s.
Applications of Refraction
- Refraction
has many applications in optics and technology. A lens uses refraction
to form an image of an object for many different purposes, such as
magnification. - A prism uses refraction to form a spectrum of colors from an incident beam of light.
- Refraction also plays an important role in the formation of a mirage and other optical illusions.
Applications of interference of waves
- Interference
is applied when creating holograms. A hologram is a photograph of an
interference pattern which is able to produce a three-dimensional image
when suitably illuminated. - Destructive interference
is used in noise reduction systems such as earphones.The system capture
sound from the environment and use computer technology to produce a
second sound wave,which leads to reduction in the loudness of the noise. - Concert
halls and auditorium are usually designed in such a way to reduce the
amount of destructive interference. Usually, the walls and ceiling made
in such a way that they absorb rather than reflect sound.
Application of wave diffraction
- Diffraction
Grating: A diffraction grating is an optical device that consists of
not one but many thousands of apertures. Spectra produced by diffraction
gratings are extremely useful in applications from studying the
structure of atoms and molecules to investigating the composition of
stars. - X-ray diffraction: X rays are light waves that have very
short wavelengths. When they irradiate a solid, crystal material they
are diffracted by the atoms in the crystal.x-ray diffraction utilises an
instrument called a diffractometer to produce diffraction patterns that
can be compared with those of known crystals to determine the structure
of new materials. - Holography: Holography is the science and
practice of making holograms. Normally, a hologram is a photographic
recording of a light field, rather than of an image formed by a lens,
and it is used to display a fully three-dimensional image of the
holographed subject, which is seen without the aid of special glasses or
other intermediate optics. An illuminating laser beam is diffracted at
specific angles, in accordance with Bragg’s law, on the surfaces of the
hologram, making it possible for an observer to see a three-dimensional
image.
The Behaviour of Waves
Demonstrate the behaviour of waves
Activity 1
Demonstrate the behaviour of waves
Behaviour
of Waves are reflection, refraction, diffraction and interference of
Waves. All waves behave in certain characteristic ways. They can
undergo: Reflection, Refraction, Diffraction and Interference.These
basic properties define the behaviour of a wave – anything that
reflects, refracts, diffracts and interferes is labelled as a wave.
of Waves are reflection, refraction, diffraction and interference of
Waves. All waves behave in certain characteristic ways. They can
undergo: Reflection, Refraction, Diffraction and Interference.These
basic properties define the behaviour of a wave – anything that
reflects, refracts, diffracts and interferes is labelled as a wave.
Propagation of Waves
The Propagation of Mechanical Waves
Describe the propagation of mechanical waves
Mechanical
waves can be divided into three main categories according to the ways
in which they travel, known aspropagation. The three propagation types
are:
waves can be divided into three main categories according to the ways
in which they travel, known aspropagation. The three propagation types
are:
- Atransverse waveis
one that vibrates at 90 degrees to the direction the wave is moving.
For example, if you hold a Slinky between two hands and shake it up and
down, you’ll get a wave that moves along the Slinky, but the vibrations
will still be up and down. Underwater waves are also transverse.
Transverse wave
- Alongitudinal
waveis one in which the vibrations are parallel to the direction the
wave is moving. That’s like sending a pulse along the length of a
Slinky, pushing it lengthwise. Instead of peaks and troughs,
longitudinal waves havecompressions(areas where the Slinky is bunched
together), andrarefactions(areas where the Slinky is spread apart).
Another example of a longitudinal wave is a sound wave. Although you
can’t see air molecules, if you could, you would notice that sound
involves air molecules hitting each other, thereby producing areas with
high densities of molecules (compressions) and areas with low densities
of molecules (rarefactions).
Longitudinal wave
- Last of all, asurface waveis
a wave that travels along the boundary between two materials. For
example the kind of water wave you most often see–along the top of
water–is an example of a surface wave. Surface waves move in similar
ways to transverse waves but are a bit more complicated in their
behavior.
Surface wave
In
the case of an earthquake, you get a mixture of all three types of
waves. The initial earthquake (called the primary wave) is longitudinal,
but the aftershock that comes later (called the secondary wave) is
transverse. Extra surface waves are also created.
the case of an earthquake, you get a mixture of all three types of
waves. The initial earthquake (called the primary wave) is longitudinal,
but the aftershock that comes later (called the secondary wave) is
transverse. Extra surface waves are also created.
The Propagation of Electromagnetic Waves
Explain the propagation of electromagnetic waves
Electromagnetic
waves are transverse waves only. Velocity of all electromagnetic waves
is equal to the velocity of light which is 300,000,000 m/s (3x10exp8).
Electromagnetic waves do not need medium for their transmission.
Electromagnetic waves are arranged in special arrangement known as
electromagnetic spectrum according to the increase in their frequencies
or decrease in their wavelengths.
waves are transverse waves only. Velocity of all electromagnetic waves
is equal to the velocity of light which is 300,000,000 m/s (3x10exp8).
Electromagnetic waves do not need medium for their transmission.
Electromagnetic waves are arranged in special arrangement known as
electromagnetic spectrum according to the increase in their frequencies
or decrease in their wavelengths.
The Relationship between Frequency, Speed and Wavelength of a Wave
Determine the relationship between frequency, speed and wavelength of a wave
Frequency
(f) of a wave is inversely proportional to its wavelength (l). Speed
(V) of a wave is constant. That is, f=V/l. That is Speed of a wave can
be expressed as a product of frequency and wavelength. That is, V = f X l
Speed of a wave is expressed in meters per second (m/s). Period (T) of a
wave is a time taken by a wave to complete one oscillation. Frequency
is a reciprocal of the Period.
(f) of a wave is inversely proportional to its wavelength (l). Speed
(V) of a wave is constant. That is, f=V/l. That is Speed of a wave can
be expressed as a product of frequency and wavelength. That is, V = f X l
Speed of a wave is expressed in meters per second (m/s). Period (T) of a
wave is a time taken by a wave to complete one oscillation. Frequency
is a reciprocal of the Period.
Mathematically it can be shown as:v = f • λ
where
- v =speed of a wave
- λ =wavelength
- f = frequency
The Refractive Index of a Medium
Determine the refractive index of a medium
Refractive
index(n) is a ratio of the velocity (Va) of a wave in air to its
velocity in a medium (Vm). n=Va/Vm. Refractive index can also be
obtained as a ratio of the sine of angle of incidence (Sin i) to the
sine of angle of refraction (Sin r). The speed of the wave depends on
the medium through which it travels. Changing the medium changes the
speed. Absolute refractive index=V in vacuum/V.
index(n) is a ratio of the velocity (Va) of a wave in air to its
velocity in a medium (Vm). n=Va/Vm. Refractive index can also be
obtained as a ratio of the sine of angle of incidence (Sin i) to the
sine of angle of refraction (Sin r). The speed of the wave depends on
the medium through which it travels. Changing the medium changes the
speed. Absolute refractive index=V in vacuum/V.
Refractive
index of a material is a measure of the change in speed of light as it
passes from a vacuum (or air as an approximation) into the material.
index of a material is a measure of the change in speed of light as it
passes from a vacuum (or air as an approximation) into the material.
In the equation above,v1is
the speed of light in a vacuum. The bigger the refractive index the
slower the light travels in that material – i.e. the smallerv2is.
the speed of light in a vacuum. The bigger the refractive index the
slower the light travels in that material – i.e. the smallerv2is.
Example 1
Light of frequency 4.6 × 1014Hz travels at a speed of 1.24 × 108ms-1in diamond.Calculate the refractive index of diamond for this colour of light.
Solution
vdiamond= 1.24 × 108ms-1
c= 3.0 × 108ms-1
(from data sheet)
Refractive index of diamond for this colour of light = 2.42
Sound Waves
Source of Sound Wave
Identify source of sound waves
Sound
is oscillation in pressure, stress, particle displacement, particle
velocity, etc., propagated in a medium with internal forces (e.g.,
elastic or viscous), or the superposition of such propagated
oscillation.
is oscillation in pressure, stress, particle displacement, particle
velocity, etc., propagated in a medium with internal forces (e.g.,
elastic or viscous), or the superposition of such propagated
oscillation.
The sources of sound
- vibrating solids.
- rapid expansion or compression (explosions and implosions).
- Smooth
(laminar) air flow around blunt obstacles may result in the formation
of vortices (the plural of vortex) that snap off or shed with a
characteristic frequency. This process is called vortex shedding and is
another means by which sound waves are formed. This is how a whistle or
flute produces sound. Also the aeolian harp effect of singing power
lines and fluttering venetian blinds.
The Concept of Audibility
Explain the concept of audibility range
Audibility
range the range of frequencies that can be heard by humans or other
animals, though it can also refer to the range of levels.
range the range of frequencies that can be heard by humans or other
animals, though it can also refer to the range of levels.
The
human range is commonly given as 20 to 20,000Hz, though there is
considerable variation between individuals, especially at high
frequencies, and a gradual loss of sensitivity to higher frequencies
with age is considered normal
human range is commonly given as 20 to 20,000Hz, though there is
considerable variation between individuals, especially at high
frequencies, and a gradual loss of sensitivity to higher frequencies
with age is considered normal
Sensitivity
also varies with frequency, as shown by equal-loudness contours.
Routine investigation for hearing loss usually involves an audiogram
which shows threshold levels relative to a normal. Several animal
species are able to hear frequencies well beyond the human hearing
range. Some dolphins and bats, for example, can hear frequencies up to
100kHz.
also varies with frequency, as shown by equal-loudness contours.
Routine investigation for hearing loss usually involves an audiogram
which shows threshold levels relative to a normal. Several animal
species are able to hear frequencies well beyond the human hearing
range. Some dolphins and bats, for example, can hear frequencies up to
100kHz.
Several
animal species are able to hear frequencies well beyond the human
hearing range. Some dolphins and bats, for example, can hear frequencies
up to 100kHz.
animal species are able to hear frequencies well beyond the human
hearing range. Some dolphins and bats, for example, can hear frequencies
up to 100kHz.
The Perception of Hearing
Describe the perception of hearing
A basic measure of hearing is afforded by an audiogram: a graph of the minimum discernible sound level at various frequencies throughout an organism’s nominal hearing range.
Behavioural
hearing tests or physiological tests can be used to find hearing
thresholds of humans and other animals. For humans, the test involves
tones being presented at a specific frequencies (pitch) and intensities
(loudness). When the subject hears the sound, he or she indicates it by
raising a hand or pressing a button. The lowest intensity they can hear
is recorded.
hearing tests or physiological tests can be used to find hearing
thresholds of humans and other animals. For humans, the test involves
tones being presented at a specific frequencies (pitch) and intensities
(loudness). When the subject hears the sound, he or she indicates it by
raising a hand or pressing a button. The lowest intensity they can hear
is recorded.
The human ear
The ear
is the organ that detects sound. It not only receives sound, but also
aids in balance and body position. The ear is part of the auditory
system.
is the organ that detects sound. It not only receives sound, but also
aids in balance and body position. The ear is part of the auditory
system.
Often
the entire organ is considered the ear, though it may also be
considered just the visible portion. In most mammals, the visible ear is
a flap of tissue that is also called the pinna (or auricle in humans) and is the first of many steps in hearing.
the entire organ is considered the ear, though it may also be
considered just the visible portion. In most mammals, the visible ear is
a flap of tissue that is also called the pinna (or auricle in humans) and is the first of many steps in hearing.
Vertebrates
have a pair of ears placed somewhat symmetrically on opposite sides of
the head. This arrangement aids in the ability to localize sound
sources.
have a pair of ears placed somewhat symmetrically on opposite sides of
the head. This arrangement aids in the ability to localize sound
sources.
The human ear is divided into three parts:
The outer ear
The
outer ear comprises the pinna (auricle), which is made of a convoluted
plate of flexible cartilage that extends as a nearly closed tube
one-third of the way down the ear canal. This outer third, which is
about eight millimetres (one-third of an inch) long, has small hairs
that point outwards to form a line of defence against small animals
creeping in. The roots of the hairs produce oils and these mix with the
secretions from nearby sweat-like glands to form the basis of wax.
outer ear comprises the pinna (auricle), which is made of a convoluted
plate of flexible cartilage that extends as a nearly closed tube
one-third of the way down the ear canal. This outer third, which is
about eight millimetres (one-third of an inch) long, has small hairs
that point outwards to form a line of defence against small animals
creeping in. The roots of the hairs produce oils and these mix with the
secretions from nearby sweat-like glands to form the basis of wax.
The
deep two-thirds of the ear canal (16 millimetres/two-thirds of an inch
long) has a bony wall lined with thin and rather fragile skin which is
devoid of glands. At the far end of the ear canal and stretched across
it is the eardrum (tympanic membrane), which forms the boundary between
the outer and middle ears.
deep two-thirds of the ear canal (16 millimetres/two-thirds of an inch
long) has a bony wall lined with thin and rather fragile skin which is
devoid of glands. At the far end of the ear canal and stretched across
it is the eardrum (tympanic membrane), which forms the boundary between
the outer and middle ears.
The middle ear (Tympanum)
The
eardrum is a circle of thin skin about eight to nine millimetres
(one-third of an inch) in diameter. Despite its name, it is not flat
like the skin of a drum, but is slightly conical with the curved sides
sloping inwards. The eardrum has three layers.
eardrum is a circle of thin skin about eight to nine millimetres
(one-third of an inch) in diameter. Despite its name, it is not flat
like the skin of a drum, but is slightly conical with the curved sides
sloping inwards. The eardrum has three layers.
The inner ear (Labyrinth)
The
inner ear is probably the most remarkably intricate piece of the body.
It makes hearing possible by converting sound into electrical impulses
that then travel along the hearing nerve (the acoustic nerve or auditory
nerve) to the brain. The inner ear also plays a major role in balance.
The balance portions of the inner ear (vestibular labyrinth) can detect
acceleration of the head in any direction whether in a straight line
(linear) or twisting and turning (angular). The electrical signals that
arise in response to head movement pass along the balance nerve
(vestibular nerve), which in due course joins with the hearing nerve to
form a single bundle (statoacoustic, vestibulo-acoustic or eighth
nerve, nerve VIII) which then enters the brain.
inner ear is probably the most remarkably intricate piece of the body.
It makes hearing possible by converting sound into electrical impulses
that then travel along the hearing nerve (the acoustic nerve or auditory
nerve) to the brain. The inner ear also plays a major role in balance.
The balance portions of the inner ear (vestibular labyrinth) can detect
acceleration of the head in any direction whether in a straight line
(linear) or twisting and turning (angular). The electrical signals that
arise in response to head movement pass along the balance nerve
(vestibular nerve), which in due course joins with the hearing nerve to
form a single bundle (statoacoustic, vestibulo-acoustic or eighth
nerve, nerve VIII) which then enters the brain.
The
portion of the inner ear that actually hears is the cochlea. This is a
hollow coiled tube set in the very dense bone called the bony labyrinth
(part of the petrous [rocklike] temporal bone). This tube is filled
with fluid, which is much the same as general body fluid (lymph) and
that which surrounds the brain (cerebrospinal fluid – CSF). This
inner-ear fluid is called perilymph. Inside the perilymph is another
coiled triangular-shaped tube called the cochlear duct (scala media),
which contains the all-important ‘hair cells’ – these convert sound into
electricity. These hair cells are arranged in two groups that follow
the coils of the cochlear duct and spiral upwards from base to apex.
There is a single row of inner hair cells (IHCs), which lie closer to
the core of the cochlea (modiolus), and three or four rows of outer hair
cells (OHCs), which are further away. In a healthy young human ear
there are about 3,500 IHCs and about 12,000 OHCs. Each hair cell has a
cluster of small rigid hairs (stereocilia), which project from the
thicker upper surface of the cell into the special fluid that fills the
cochlear duct. This fluid is called endolymph and is remarkable in that
it has a strongly positive electrical charge associated with it – about
80 millivolts – and is rich in potassium, a metallic element.
portion of the inner ear that actually hears is the cochlea. This is a
hollow coiled tube set in the very dense bone called the bony labyrinth
(part of the petrous [rocklike] temporal bone). This tube is filled
with fluid, which is much the same as general body fluid (lymph) and
that which surrounds the brain (cerebrospinal fluid – CSF). This
inner-ear fluid is called perilymph. Inside the perilymph is another
coiled triangular-shaped tube called the cochlear duct (scala media),
which contains the all-important ‘hair cells’ – these convert sound into
electricity. These hair cells are arranged in two groups that follow
the coils of the cochlear duct and spiral upwards from base to apex.
There is a single row of inner hair cells (IHCs), which lie closer to
the core of the cochlea (modiolus), and three or four rows of outer hair
cells (OHCs), which are further away. In a healthy young human ear
there are about 3,500 IHCs and about 12,000 OHCs. Each hair cell has a
cluster of small rigid hairs (stereocilia), which project from the
thicker upper surface of the cell into the special fluid that fills the
cochlear duct. This fluid is called endolymph and is remarkable in that
it has a strongly positive electrical charge associated with it – about
80 millivolts – and is rich in potassium, a metallic element.
The
hair cells in their rows are grouped together with their supporting
cells in the organ of Corti. This is a small ridge that sits on a thin,
very flexible membrane called the basilar membrane. The basilar membrane
forms the floor of the triangular cochlear duct. The sloping roof is
another very thin membrane (Reissner’s membrane) and the side wall is a
thickened region rich in blood vessels (the stria vascularis). This
structure is responsible for maintaining the composition of the rather
unusual and very important endolymph.
hair cells in their rows are grouped together with their supporting
cells in the organ of Corti. This is a small ridge that sits on a thin,
very flexible membrane called the basilar membrane. The basilar membrane
forms the floor of the triangular cochlear duct. The sloping roof is
another very thin membrane (Reissner’s membrane) and the side wall is a
thickened region rich in blood vessels (the stria vascularis). This
structure is responsible for maintaining the composition of the rather
unusual and very important endolymph.
Adjacent
to the base of the hair cells are the nerves that carry impulses to the
brain (the afferent nerves). At least 90 per cent of these nerves come
from the inner hair cells, despite their smaller number. Each inner hair
cell has about 10 nerve endings attached to it and there are,
therefore, about 30,000 nerve fibres in the acoustic nerve.
to the base of the hair cells are the nerves that carry impulses to the
brain (the afferent nerves). At least 90 per cent of these nerves come
from the inner hair cells, despite their smaller number. Each inner hair
cell has about 10 nerve endings attached to it and there are,
therefore, about 30,000 nerve fibres in the acoustic nerve.
The
hearing nerves travel inwards, along with the balance and facial
nerves, through a canal in the inner part of the skull (variously called
the internal auditory meatus [IAM], internal auditory canal [IAC] or
porus acousticus) to reach the brain stem. This part of the brain deals
with lots of automatic functions such as pulse, blood pressure, general
alertness, balance, and so on.
hearing nerves travel inwards, along with the balance and facial
nerves, through a canal in the inner part of the skull (variously called
the internal auditory meatus [IAM], internal auditory canal [IAC] or
porus acousticus) to reach the brain stem. This part of the brain deals
with lots of automatic functions such as pulse, blood pressure, general
alertness, balance, and so on.
About
half of the hearing nerves from each ear cross over to the other side
of the brain stem and then, on both sides, the nerves pass up the brain
stem through the midbrain, eventually to reach ‘consciousness’ in what
is called the cortex of the brain. For hearing, this conscious region
is located in the temporal lobe portion of the brain, which lies on each
side of the head just above the ear.
half of the hearing nerves from each ear cross over to the other side
of the brain stem and then, on both sides, the nerves pass up the brain
stem through the midbrain, eventually to reach ‘consciousness’ in what
is called the cortex of the brain. For hearing, this conscious region
is located in the temporal lobe portion of the brain, which lies on each
side of the head just above the ear.
The Concept of Echo and Reverberation
Explain the concept of echo and reverberation
Echo
An echo occurs when asound wave is reflected and hence arrives to the listener after some time delay after the direct sound.
When
we are in a empty space surrounded by mountains and we shout loudly, we
see that faint sound resembling the original sound coming back after
some delay of time. This perception of the reflected wave is nothing but
the echo. This is experienced in remote places, in rooms that are big
and empty, in caves, buildings
we are in a empty space surrounded by mountains and we shout loudly, we
see that faint sound resembling the original sound coming back after
some delay of time. This perception of the reflected wave is nothing but
the echo. This is experienced in remote places, in rooms that are big
and empty, in caves, buildings
Echo
is derived from the Greek word which means Sound.The echo is produced
due to hitting of the sound waves with the obstacles which makes the
sound to reflect back
is derived from the Greek word which means Sound.The echo is produced
due to hitting of the sound waves with the obstacles which makes the
sound to reflect back
Application of Echo:
Measuring distance
By knowing the speed of sound and measuring the time it takes to hear the echo, you can calculate the distance of the object. A
sonar device sends out a sound and automatically calculates the
distance of an object. Submarines use sonar to find objects under the
water, including other submarines. The “ping” sound heard in a submarine
comes from the sonar device sending out a sound wave under water.
sonar device sends out a sound and automatically calculates the
distance of an object. Submarines use sonar to find objects under the
water, including other submarines. The “ping” sound heard in a submarine
comes from the sonar device sending out a sound wave under water.
Fishermen
also use sonar to find schools of fish. Since this is an electronic
device, the time it takes for the wave to return can be much less than
the 0.1 second required to hear an echo. For example, if the speed of
sound in water is 1500 m/s and the fisherman’s sonar device detects an
echo in 0.02s, the distance of the object under water will bed = v x t = 1500 m/s x 0.02s = 30 m (back and forth).
also use sonar to find schools of fish. Since this is an electronic
device, the time it takes for the wave to return can be much less than
the 0.1 second required to hear an echo. For example, if the speed of
sound in water is 1500 m/s and the fisherman’s sonar device detects an
echo in 0.02s, the distance of the object under water will bed = v x t = 1500 m/s x 0.02s = 30 m (back and forth).
That
may mean a school of fish are 15 meters away. Sonar and radar work on
the same principle. Sonar uses sound waves, while radar uses
electromagnetic waves.
may mean a school of fish are 15 meters away. Sonar and radar work on
the same principle. Sonar uses sound waves, while radar uses
electromagnetic waves.
Velocity
When
a wave bounces off a moving object, the frequency of the sound changes,
according to the relative velocity of the object. (Velocity is the
measurement of speed and direction). If the object is moving toward you,
the frequency or pitch of the sound gets higher. When it is moving
away, the pitch gets lower. The faster the object is moving, the greater
the change in frequency or pitch. This is called the Doppler Effect.
a wave bounces off a moving object, the frequency of the sound changes,
according to the relative velocity of the object. (Velocity is the
measurement of speed and direction). If the object is moving toward you,
the frequency or pitch of the sound gets higher. When it is moving
away, the pitch gets lower. The faster the object is moving, the greater
the change in frequency or pitch. This is called the Doppler Effect.
You
have probably experienced the Doppler Effect when you heard how the
sound of an ambulance siren changes pitch as it passes by. The Doppler
Effect can be used to measure the velocity of an object by comparing the
frequency of the sound sent out to the frequency of the sound reflected
by in the echo. A sonar device is usually used to calculate the
velocity of the object.
have probably experienced the Doppler Effect when you heard how the
sound of an ambulance siren changes pitch as it passes by. The Doppler
Effect can be used to measure the velocity of an object by comparing the
frequency of the sound sent out to the frequency of the sound reflected
by in the echo. A sonar device is usually used to calculate the
velocity of the object.
Note:
Doppler radar works on a similar principle to measure the speed of
storms in weather prediction, except that it uses echoes from
electromagnetic waves.
Doppler radar works on a similar principle to measure the speed of
storms in weather prediction, except that it uses echoes from
electromagnetic waves.
Bats can find moths
Bats
use echoes to find good tasting moths, while flying around at night.
The bat sends a sharp click or chirping sound and then hears and
processes any echoes off other objects in the area. Bats have large ears
that are very sensitive to sounds in certain wavelengths
use echoes to find good tasting moths, while flying around at night.
The bat sends a sharp click or chirping sound and then hears and
processes any echoes off other objects in the area. Bats have large ears
that are very sensitive to sounds in certain wavelengths
Reverberation
Reverberations
are the collection of reflected sounds from the surfaces in an
enclosure like an auditorium. It is a desirable property of auditoriums
to the extent that it helps to overcome the inverse square law drop off
of sound intensity in the enclosure.
are the collection of reflected sounds from the surfaces in an
enclosure like an auditorium. It is a desirable property of auditoriums
to the extent that it helps to overcome the inverse square law drop off
of sound intensity in the enclosure.
However, if it is excessive, it makes the sounds run together with loss of articulation – the sound becomes muddy, garbled.
A reverberation is the same as echo but the distance here is less.The distance between the source of the sound and the obstacle by which it is reflected is less in Reverberation.Here, in reverberation the time delay is less than 0.1 second.
The
reflected wave reaches the observer in less than 0.1 second. Now as the
delay in time is less than the original sound is still in memory, the
delay between perception of sound and the original sound is very-very
less.
reflected wave reaches the observer in less than 0.1 second. Now as the
delay in time is less than the original sound is still in memory, the
delay between perception of sound and the original sound is very-very
less.
Question Time 1
How is an Echo Different from the reverberation?
Echo
is when long distances are considered and reverberation is when short
distances are considered. Echo is due to the reflection of sound wave by
obstacles or end points like wall etc. But Reverberation is due to the
collection of reflection sounds from the surface which is enclosed
completely.
is when long distances are considered and reverberation is when short
distances are considered. Echo is due to the reflection of sound wave by
obstacles or end points like wall etc. But Reverberation is due to the
collection of reflection sounds from the surface which is enclosed
completely.
The Speed of Sound in Air
Determine the speed of sound in air
Sound
can travel in air (gases), liquids and in solids. Sound is a mechanical
wave hence can not travel in vacuum. The speed of sound in air is
approximately 340 m/s. The speed of sound in air changes with
temperature. As the temperature increase the speed of sound also
increases. Sound travel faster in solids than in liquids and air.
can travel in air (gases), liquids and in solids. Sound is a mechanical
wave hence can not travel in vacuum. The speed of sound in air is
approximately 340 m/s. The speed of sound in air changes with
temperature. As the temperature increase the speed of sound also
increases. Sound travel faster in solids than in liquids and air.
Musical Sound
The Concept of a Musical Sound
Explain the concept of a musical sound
Music
is organised sound which has some pattern. Music uses certain
frequencies or combinations of frequencies called the musical scale to
produce sounds that are generally appealing to the human ear.
is organised sound which has some pattern. Music uses certain
frequencies or combinations of frequencies called the musical scale to
produce sounds that are generally appealing to the human ear.
Noise
on the other hand, is random and without structure. Any and all
frequencies might occur and their combination is often not appealing to
the ear.
on the other hand, is random and without structure. Any and all
frequencies might occur and their combination is often not appealing to
the ear.
Factors Affecting Loudness, Pitch and Quality of Musical Sound
Identify factors affecting loudness, pitch and quality of a musical sound
The
musical sounds produced by different musical instruments have distinct
properties that are used to describe them. These include loudness, pitch
and timbre:
musical sounds produced by different musical instruments have distinct
properties that are used to describe them. These include loudness, pitch
and timbre:
- Loudness:loudness is the intensity of the sound which is the perceptual property.
It is determined by the amplitude of sound wave and the number of
auditory nerves activated by sound wave. Amplitude is a physical
property determined by how much air pressure in a compression or
rarefaction deviates from normal air pressure. The larger the amplitude
the louder the sound. - Pitch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based on the frequency
of sound wave vibration. Frequency is an objective, scientific concept,
whereas pitch is subjective. Sound waves themselves do not have pitch.
It takes a human brain to map the internal quality of pitch.-Pitches are
usually quantified as frequencies in cycles per second, or hertz. - Timbre is
the tone quality of sound produced by an instrument. It is referred to
as sound quality or sound colour and it is a perceptual property. What
makes a particular musical sound different from another, even when they
have the same pitch and loudness.
Different Musical Instruments
Identify the different musical instruments
Musical
instrument are the device constructed or modified for the purpose of
making music. They are categorizied into three categories:
instrument are the device constructed or modified for the purpose of
making music. They are categorizied into three categories:
- Wind Instruments:This
class of musical instruments requires you to blow into a specific wind
instrument by following an order to ensure that the sound that you
desire is produced. The instruments can be expected to work depending on
the principles of frequencies, sound waves, acoustics, resonance and
harmonics. The pitch of the produced sound when you start blowing the
instrument is actually dependent on the length of the air column through
which the waves of the sounds vibrate.Some of the most popular wind
instruments are piccolo, flute, clarinet, shakuhachi, bassoon, oboe,
accordion, English horn, harmonica, saxophone, pianica, bagpie and
shehnai. - Percussion Instruments:These
instruments require you to strike the surface of the instrument to
generate vibrations to produce your desired note. Percussion instruments
can actually be divided into two types. The first type includes tuned instruments
that are known to produce a definite pitch or a series of different
pitches. Some examples of the tuned percussion instruments include
xylophone, vibraphone, marimba, tubular bells and timpani or kettle
drum. The second type of percussion instruments is the indefinite pitch. Its examples include triangle, castanets, rattle, cymbals, tambourine, anvil and gong. - String Instruments:
These are composed of those instruments that work based on sound wave
vibrations produced by strings. The pitch that can be produced by these
instruments is dependent on the length of air column and the type and
thickness of strings used.Among the most popular string instruments are
guitar, viola, violin, cello, mandolin, harp, double bass and banjo.
The Terms Stationary Wave, Nodes and Antinodes
Explain the terms stationary wave, nodes and antinodes
Stationary wave
Is a wave in a medium in which each point on the axis of the wave has an associated constant amplitude
This
phenomenon can occur because the medium is moving in the opposite
direction to the wave, or it can arise in a stationary medium as a
result of interference between two waves traveling in opposite
directions.
phenomenon can occur because the medium is moving in the opposite
direction to the wave, or it can arise in a stationary medium as a
result of interference between two waves traveling in opposite
directions.
The
most common cause of standing waves is the phenomenon of resonance, in
which standing waves occur inside a resonator due to interference
between waves reflected back and forth at the resonator’s resonant
frequency.
most common cause of standing waves is the phenomenon of resonance, in
which standing waves occur inside a resonator due to interference
between waves reflected back and forth at the resonator’s resonant
frequency.
For
waves of equal amplitude traveling in opposing directions, there is on
averageno net propagation of energy.Traveling waves have high points
called crests and low points called troughs (in the transverse case) or
compressed points called compressions and stretched points called
rarefactions (in the longitudinal case) that travel through the medium.
waves of equal amplitude traveling in opposing directions, there is on
averageno net propagation of energy.Traveling waves have high points
called crests and low points called troughs (in the transverse case) or
compressed points called compressions and stretched points called
rarefactions (in the longitudinal case) that travel through the medium.
Standing
waves don’t go anywhere, but they do have regions where the disturbance
of the wave is quite small, almost zero. These locations are called
nodes. There are also regions where the disturbance is quite intense,
greater than anywhere else in the medium, called antinodes.
waves don’t go anywhere, but they do have regions where the disturbance
of the wave is quite small, almost zero. These locations are called
nodes. There are also regions where the disturbance is quite intense,
greater than anywhere else in the medium, called antinodes.
Nodes
The locations at which the amplitude is minimum are called nodes.
Antinodes
The locations where the amplitude is maximum are called antinodes.
The Frequency of a Musical Note
Determine the frequency of a musical note
The
frequency of a musical note is affected by length of vibrating string
and the velocity of the waves. Velocity of the waves depends on the
tension on the string and the linear mass density. The linear mass
density is the mass per unit length. The frequency of a music note
depends on the length, mass per unit length and the tension.
frequency of a musical note is affected by length of vibrating string
and the velocity of the waves. Velocity of the waves depends on the
tension on the string and the linear mass density. The linear mass
density is the mass per unit length. The frequency of a music note
depends on the length, mass per unit length and the tension.
The Difference between the Fundamental Note and Overtones
Distinguish between the fundamental note and overtones
Fundamental Note
Fundamental
note is the lowest resonant frequency of a vibrating object. Most
vibrating objects have more than one resonant frequency and those used
in musical instruments typically vibrate at harmonics of the
fundamental.
note is the lowest resonant frequency of a vibrating object. Most
vibrating objects have more than one resonant frequency and those used
in musical instruments typically vibrate at harmonics of the
fundamental.
A
harmonic is defined as an integer (whole number),n multiple of the
fundamental frequency. Vibrating strings, open cylindrical air columns,
and conical air columns will vibrate at all harmonics of the
fundamental.
harmonic is defined as an integer (whole number),n multiple of the
fundamental frequency. Vibrating strings, open cylindrical air columns,
and conical air columns will vibrate at all harmonics of the
fundamental.
Overnote
An overtone
is any frequency higher than the fundamental frequency of a sound.
Using the model of Fourier analysis, the fundamental and the overtones
together are called partials.Harmonics, or more precisely, harmonic
partials, are partials whose frequencies are integer multiples of the
fundamental (including the fundamental which is 1 times itself). These
overlapping terms are variously used when discussing the acoustic
behavior of musical instruments.
is any frequency higher than the fundamental frequency of a sound.
Using the model of Fourier analysis, the fundamental and the overtones
together are called partials.Harmonics, or more precisely, harmonic
partials, are partials whose frequencies are integer multiples of the
fundamental (including the fundamental which is 1 times itself). These
overlapping terms are variously used when discussing the acoustic
behavior of musical instruments.
There are integer multiples of a certain frequency (fundamental), that are called harmonics, partial tones (partials) or overtones.It
is important to note that the term ‘overtones’ does not include the
fundamental frequency. The first overtone is therefore already the
second harmonic or the second partial. The term overtone should never be
mixed with the other terms, as the counting is unequal.The term
harmonic has a precise meaning – that of an integer (whole number)
multiple of the fundamental frequency of a vibrating object.
is important to note that the term ‘overtones’ does not include the
fundamental frequency. The first overtone is therefore already the
second harmonic or the second partial. The term overtone should never be
mixed with the other terms, as the counting is unequal.The term
harmonic has a precise meaning – that of an integer (whole number)
multiple of the fundamental frequency of a vibrating object.
The Concept of Resonance as Applied to Sound
Explain the concept of resonance as applied to sound
Resonance
is a phenomenon that occurs when a given system is driven by another
vibrating system or external force to oscillate with greater amplitude
at a specific preferential frequency.Frequencies at which the response
amplitude is a relative maximum are known as the system’s resonant frequencies, or resonance frequencies.
is a phenomenon that occurs when a given system is driven by another
vibrating system or external force to oscillate with greater amplitude
at a specific preferential frequency.Frequencies at which the response
amplitude is a relative maximum are known as the system’s resonant frequencies, or resonance frequencies.
At
resonant frequencies, small periodic driving forces have the ability to
produce large amplitude oscillations. This is because the system stores
vibrational energy. Resonance occurs when a system is able to store and
easily transfer energy between two or more different storage modes
(such as kinetic energy and potential energy in the case of a pendulum).
resonant frequencies, small periodic driving forces have the ability to
produce large amplitude oscillations. This is because the system stores
vibrational energy. Resonance occurs when a system is able to store and
easily transfer energy between two or more different storage modes
(such as kinetic energy and potential energy in the case of a pendulum).
However, there are some losses from cycle to cycle, called damping.
When damping is small, the resonant frequency is approximately equal to
the natural frequency of the system, which is a frequency of unforced
vibrations. Some systems have multiple, distinct, resonant frequencies.
When damping is small, the resonant frequency is approximately equal to
the natural frequency of the system, which is a frequency of unforced
vibrations. Some systems have multiple, distinct, resonant frequencies.
Resonance in Closed Ended Pipes
A
closed ended instrument has one end closed off, and the other end open.
An example would be an instrument like some organ pipes (although in
some designs they are open), or a flute.
closed ended instrument has one end closed off, and the other end open.
An example would be an instrument like some organ pipes (although in
some designs they are open), or a flute.
Although
you blow in through the mouth piece of a flute, the opening you’re
blowing into isn’t at the end of the pipe, it’s along the side of the
flute. The end of the pipe is closed off near the mouth piece. Remember
that it is actually air that is doing the vibrating as a wave here.
you blow in through the mouth piece of a flute, the opening you’re
blowing into isn’t at the end of the pipe, it’s along the side of the
flute. The end of the pipe is closed off near the mouth piece. Remember
that it is actually air that is doing the vibrating as a wave here.
- The
air at the closed end of the pipe must be a node (not moving), since
the air is not free to move there and must be able to be reflected back. - There must also be an antinode where the opening is, since that is where there is maximum movement of the air.
- The simplest, smallest wave that I can possibly fit in a closed end pipe is shown in Figure below.
- Notice
how even though it has been flipped left-to-right and it looks squished
and stretched a bit to fit, this is still ¼ of a wavelength. - Since this is the smallest stable piece of a wave I can fit in this pipe, this is the Fundamental, or 1st Harmonic.
Since
the length of the tube is the same as the length of the ¼ wavelength I
know that the length of this tube is ¼ of a wavelength… this leads to
our first formula: L = ¼ λ
the length of the tube is the same as the length of the ¼ wavelength I
know that the length of this tube is ¼ of a wavelength… this leads to
our first formula: L = ¼ λ
- “L” is the length of the tube in meters. On it’s own this formula really doesn’t help us much.
- Instead, we have to solve this formula for λ and then combine it with the formula v=fλ to get a more useful formula:
When
the wave reaches the closed end it’s going to be reflected as an
inverted wave (going from air to whatever the pipe is made of is a
pretty big change so this is what we would expect). It would look like
Figure above.
the wave reaches the closed end it’s going to be reflected as an
inverted wave (going from air to whatever the pipe is made of is a
pretty big change so this is what we would expect). It would look like
Figure above.
This
does not change the length of the wave in our formula, since we are
only seeing the reflection of the wave that already exists in the pipe.
does not change the length of the wave in our formula, since we are
only seeing the reflection of the wave that already exists in the pipe.
What does the next harmonic look like? It’s the 3rd Harmonic.
- I
know this name might seem a little confusing (I’m the first to agree
with you!) but because of the actual notes produced and the way the
waves fit in, musicians refer to the next step up in a closed end pipe
instrument as the 3rd harmonic… there is no such thing as a 2nd harmonic for closed end pipes. - In fact, all of the harmonics in closed end pipes are going to be odd numbers.
Remember
that we have to have an antinode at the opening (where the air is
moving) and a node at the closed end (where the air can’t move). That
means for the 3rd harmonic we get something like Figure above. This is ¾ of a wavelength fit into the tube, so the length of the tube is… L = ¾ λ
that we have to have an antinode at the opening (where the air is
moving) and a node at the closed end (where the air can’t move). That
means for the 3rd harmonic we get something like Figure above. This is ¾ of a wavelength fit into the tube, so the length of the tube is… L = ¾ λ
This is the third harmonic of the closed end pipe. The formula for the frequency of the note we will hear is…
Do
you notice a pattern forming in the formulas? Hopefully, because for
both open and closed end pipes, we will only give you the formulas for
the fundamentals lengths. You need to remember how to get the rest.
you notice a pattern forming in the formulas? Hopefully, because for
both open and closed end pipes, we will only give you the formulas for
the fundamentals lengths. You need to remember how to get the rest.
If we drew in the reflection of the third harmonic it would look like Figure below.
One more to make sure you see the pattern. The 5th Harmonic (fig. above)
There is one full wavelength
in there (4/4) plus an extra ¼ of a wavelength for a total of 5/4. The
length of the pipe is… L = 5/4 λ And the note produced by the 5th Harmonic is found using the formula…f = 5v/4L
in there (4/4) plus an extra ¼ of a wavelength for a total of 5/4. The
length of the pipe is… L = 5/4 λ And the note produced by the 5th Harmonic is found using the formula…f = 5v/4L
Figure below shows the reflection of a 5th Harmonic for a closed end pipe.
Open End Pipes
An
open ended instrument has both ends open to the air. An example would
be an instrument like a trumpet. You blow in through one end and the
sound comes out the other end of the pipe.
open ended instrument has both ends open to the air. An example would
be an instrument like a trumpet. You blow in through one end and the
sound comes out the other end of the pipe.
Fundamental
- The fundamental (first harmonic) for an open end pipe needs to be an antinode at both ends, since the air can move at both ends.
- That’s why the smallest wave we can fit in is shown in Figure 11.
- This looks different than the ½ wavelength that I showed you in Figure 3, but it is still half of a full wavelength.
- That means the length of the tube and frequency formulas are…L = ½ λ
f = v/2L
2nd Harmonic
The next note we can play is the 2nd harmonic.
- Yep, open end pipes have a 2nd harmonic… they can have any number harmonic they want, odd or even.
- Again, it kind of looks weird, but trace it out and you’ll see that there is exactly one wavelength here.
- The length and frequency formulas are…L = 2/2 λ, f= 2v/2L
I’m not going to show you what the 3rd harmonic looks like. Instead, try drawing it yourself and see what you get.
As a hint to help you, the formulas for the length and frequency are…L = 3/2 λ, f = 3v/2L
A Simple Musical Instrument
Construct a simple musical instrument
A
musical instrument is a device constructed for making music. There are
three categories of musical instruments: string, percussion and wind
instruments. The note of a musical instrument depends on five
parameters: pitch, frequency, intensity, loudness and quality of a music
note. Pitch of a note is its position in the musical scale and depends
on the frequency of the vibration of the wave.
musical instrument is a device constructed for making music. There are
three categories of musical instruments: string, percussion and wind
instruments. The note of a musical instrument depends on five
parameters: pitch, frequency, intensity, loudness and quality of a music
note. Pitch of a note is its position in the musical scale and depends
on the frequency of the vibration of the wave.
Activity 2
Construct a simple musical instrument
