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Particle displacement

 

 
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Particle displacement
 
 
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Particle displacement or particle amplitude (represented in mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 by the lower-case Greek letter
Greek alphabet

The Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the late 9th century BC or early 8th century BCE....
 ξ
Xi

Xi is the 14th letter of the Greek alphabet. It is in Modern Greek, and generally or in English language. In the system of Greek numerals, it has a value of 60....
) is a measurement
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
 of distance
Distance

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria ....
 (in metre
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
s) of the movement of a particle in a medium as it transmits a wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
. In most cases this is a longitudinal wave
Longitudinal wave

Longitudinal waves are waves that have vibrations along or parallel to their direction of travel; that is, waves in which the motion of the medium is in the same direction as the motion of the wave....
 of pressure (such as sound
Sound

Sound is vibration transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a threshold of hearing to be heard, or the sensation stimulated in organs of hearing by such vibrations....
), but it can also be a transverse wave
Transverse wave

A transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer. If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the y-z plane....
, such as the vibration
Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and Alternating current power....
 of a taut string. In the case of a sound wave travelling through air
AIR

Air is the part of Earth's atmosphere that humans breath and as such Air .Air may also refer to:...
, the particle displacement is evident in the oscillation
Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and Alternating current power....
s of air molecule
Molecule

In chemistry, a molecule is defined as a sufficiently stable, electric charge neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds....
s with, and against, the direction in which the sound wave is travelling.






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Particle displacement or particle amplitude (represented in mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 by the lower-case Greek letter
Greek alphabet

The Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the late 9th century BC or early 8th century BCE....
 ξ
Xi

Xi is the 14th letter of the Greek alphabet. It is in Modern Greek, and generally or in English language. In the system of Greek numerals, it has a value of 60....
) is a measurement
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
 of distance
Distance

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria ....
 (in metre
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
s) of the movement of a particle in a medium as it transmits a wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
. In most cases this is a longitudinal wave
Longitudinal wave

Longitudinal waves are waves that have vibrations along or parallel to their direction of travel; that is, waves in which the motion of the medium is in the same direction as the motion of the wave....
 of pressure (such as sound
Sound

Sound is vibration transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a threshold of hearing to be heard, or the sensation stimulated in organs of hearing by such vibrations....
), but it can also be a transverse wave
Transverse wave

A transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer. If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the y-z plane....
, such as the vibration
Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and Alternating current power....
 of a taut string. In the case of a sound wave travelling through air
AIR

Air is the part of Earth's atmosphere that humans breath and as such Air .Air may also refer to:...
, the particle displacement is evident in the oscillation
Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and Alternating current power....
s of air molecule
Molecule

In chemistry, a molecule is defined as a sufficiently stable, electric charge neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds....
s with, and against, the direction in which the sound wave is travelling. A particle of the medium undergoes displacement according to the particle velocity
Particle velocity

Particle velocity is the velocity v of a particle in a Transmission medium as it transmits a wave. In many cases this is a longitudinal wave of pressure as with sound, but it can also be a transverse wave as with the vibration of a taut string....
 of the wave traveling through the medium, while the sound wave itself moves at the speed of sound
Speed of sound

Sound is a vibration that travels through an elasticity medium as a wave. The speed of sound describes how much distance such a wave travels in a certain amount of time....
, equal to 343 m/s in air at 20 °C.

The instantaneous particle displacement ? in m for a wave is:

If the wave is a standing wave or a traveling wave containing a single frequency, the particle displacement is:

This expression for undergoes simple harmonic oscillation, and as such is usually expressed as an rms
RMS

RMS may refer to:...
 time average.

Particle displacement for a traveling wave containing a single frequency can be represented in terms of other measurements:

where in the above equation, the quantities may be taken throughout as rms time-averages (or all as maximum values). The single frequency traveling wave has acoustic impedance equal to the characteristic impedance, . Further representations for can be found from the above equations using the replacement .

Symbol Units Meaning
? m, meters Particle displacement
v m/s particle velocity
Particle velocity

Particle velocity is the velocity v of a particle in a Transmission medium as it transmits a wave. In many cases this is a longitudinal wave of pressure as with sound, but it can also be a transverse wave as with the vibration of a taut string....
? = 2pf radians/s
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
 		 angular frequency
Angular frequency

In physics , angular frequency ? is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity....
f Hz, hertz
Hertz

The hertz is a measure of frequency per unit of time, or the number of list of cycles per second. It is the SI base unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts....
 		 frequency
Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
p Pa, pascal
Pascal (unit)

The pascal is the SI derived unit of pressure, stress , Young's modulus and tensile strength. It is a measure of force per unit area i.e. equivalent to one newton per square meter or one joule per cubic meter....
s 		sound pressure
Sound pressure

Sound pressure is the local pressure deviation from the ambient pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water....
Z0 = c · ? N
Newton

The newton is the International System of Units SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics....
·s
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
/m
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
3 		characteristic impedance
Characteristic impedance

The characteristic impedance or surge impedance of a uniform transmission line, usually written , is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections....
Z = p / v N
Newton

The newton is the International System of Units SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics....
·s
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
/m
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
3 		acoustic impedance
Acoustic impedance

The acoustic impedance Z is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments....
c m
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
/s
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
 		 Speed of sound
Speed of sound

Sound is a vibration that travels through an elasticity medium as a wave. The speed of sound describes how much distance such a wave travels in a certain amount of time....
? kg
Kilogram

The kilogram or kilogrammeThe spelling kilogram is used by the International Committee for Weights and Measures and the U.S....
/m
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
3 		Density of air
Density of air

The density of air, ? , is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics and other sciences. Air density decreases with increasing altitude, as does air pressure....
I W
WATT

WATT is a radio station broadcasting a News radio-Talk radio-Sports radio format. Licensed to Cadillac, Michigan, it first began broadcasting in 1945....
/m2 		sound intensity
Sound intensity

The sound intensity, I, is defined as the sound power Pac per unit area A. The usual context is the noise measurement of sound intensity in the air at a listener's location....
E W
WATT

WATT is a radio station broadcasting a News radio-Talk radio-Sports radio format. Licensed to Cadillac, Michigan, it first began broadcasting in 1945....
·s
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
/m
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
3 		sound energy density
Sound energy density

The sound energy density or sound density is an adequate measure to describe the sound field at a given point as a sound energy value. The letter "lower case w" sign is easily mixed with the sign , therefore we choose the letter E....
Pac W, watt
WATT

WATT is a radio station broadcasting a News radio-Talk radio-Sports radio format. Licensed to Cadillac, Michigan, it first began broadcasting in 1945....
s 		sound power
Sound power

Sound power or acoustic power Pac is a measure of sound energy E per time t unit.It is measured in watts, or sound intensity I times area A:...
 or acoustic power
A m
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
2 		Area
Area

Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron....
a m
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
/s
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
2 		Particle acceleration
Particle acceleration

In a compressible sound transmission medium - mainly air - air particles get an accelerated motion: the particle acceleration or sound acceleration with the symbol a in metre per second squared....


See also


  • Wave
    Wave

    A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
  • Sound particle
    Sound particle

    Sound particle is a Quantum mechanical description tool for the advancing pressure wave within the medium that creates sound. Sound particles are a private case of the more general phenomenon in quantum mechanics called phonons...


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