Particle velocity
Encyclopedia
Particle velocity is the velocity v of a particle (real or imagined) in a 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.
When applied to a sound wave through a medium of a fluid like air, particle velocity would be the physical speed of a parcel of fluid as it moves back and forth in the direction the sound wave is travelling as it passes.
Particle velocity should not be confused with the speed of the wave
as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the speed of sound
. The wave moves relatively fast, while the particles oscillate around their original position with a relatively small particle velocity. Particle velocity should also not be confused with the velocity of individual molecules.
In applications involving sound, the particle velocity is usually measured using a logarithmic decibel
scale called particle velocity level.
and acceleration for single frequency plane wave of frequency f using
It is further related to the instantaneous acoustic intensity vector I (not the time-averaged acoustic intensity) according to
It shows the ratio of the particle velocity v1 and the particle velocity v0.
The particle velocity level is:
where v1 and v0 are the velocities.
The particle velocity level has the letter "Lv".
The unit
of the particle velocity level is named "dB".
Notice: The dB
is dimensionless.
If v0 is the standard reference particle velocity of:
we use "dB SVL". (SVL = sound velocity level).
Sound particle velocity v should not be confused with Sound velocity c.
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
as it transmits a wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
. In many cases this is a longitudinal wave
Longitudinal wave
Longitudinal waves, as known as "l-waves", are waves that have the same direction of vibration as their direction of travel, which means that the movement of the medium is in the same direction as or the opposite direction to the motion of the wave. Mechanical longitudinal waves have been also...
of pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
as with sound, 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...
as with the vibration of a taut string.
When applied to a sound wave through a medium of a fluid like air, particle velocity would be the physical speed of a parcel of fluid as it moves back and forth in the direction the sound wave is travelling as it passes.
Particle velocity should not be confused with the speed of the wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
. The wave moves relatively fast, while the particles oscillate around their original position with a relatively small particle velocity. Particle velocity should also not be confused with the velocity of individual molecules.
In applications involving sound, the particle velocity is usually measured using a logarithmic decibel
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
scale called particle velocity level.
Equations in terms of other measurements
The velocity v can be related to the particle displacement and acceleration for single frequency plane wave of frequency f usingIt is further related to the instantaneous acoustic intensity vector I (not the time-averaged acoustic intensity) according to
| Symbol | Units | Meaning |
|---|---|---|
| v | m/s | particle velocity |
| ξ | m, meters | particle displacement Particle displacement Particle displacement or particle amplitude is a measurement of distance of the movement of a particle from its equilibrium position in a medium as it transmits a wave.... |
| ω = 2πf | radians/s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... |
angular frequency Angular frequency In physics, angular frequency ω 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 the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications.... |
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, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre... s |
sound pressure Sound pressure Sound pressure or acoustic pressure is the local pressure deviation from the ambient atmospheric pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water... |
| Z | N·s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... /m³ |
acoustic impedance Acoustic impedance The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given air vibration at that frequency. The acoustic impedance Z is frequency dependent and is very useful, for example, for describing the behaviour of musical wind instruments... |
| E | W Watt The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:... ·s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... /m³ |
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... |
| Pac | W, watt Watt The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:... s |
sound power or acoustic power |
| A | m² | area Area Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat... |
| a | m/s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... 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/second². In acoustics or physics, acceleration is defined as the rate of change of velocity. It is thus a vector... |
 |
Kg/m M M is the thirteenth letter of the basic modern Latin alphabet.-History:The letter M is derived from the Phoenician Mem, via the Greek Mu . Semitic Mem probably originally pictured water... 3 |
Air Density |
Particle velocity level
The particle velocity level or the sound velocity level tells the ratio of a sound incidence in comparison to a reference level of 0 dB in a medium, mostly air.It shows the ratio of the particle velocity v1 and the particle velocity v0.
The particle velocity level is:
where v1 and v0 are the velocities.
The particle velocity level has the letter "Lv".
The unit
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...
of the particle velocity level is named "dB".
Notice: The dB
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
is dimensionless.
If v0 is the standard reference particle velocity of:
we use "dB SVL". (SVL = sound velocity level).
Sound particle velocity v should not be confused with Sound velocity c.
See also
- Sound particleSound particleSound particleIn the context of particle displacement, particle velocity, etc, an imaginary infinitesimal volume of a medium that shares the movement of the medium in response to the presence of sound at a specified point or in a specified region...
- Particle displacementParticle displacementParticle displacement or particle amplitude is a measurement of distance of the movement of a particle from its equilibrium position in a medium as it transmits a wave....
- Particle accelerationParticle accelerationIn 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/second². In acoustics or physics, acceleration is defined as the rate of change of velocity. It is thus a vector...
- Pressure gradientPressure gradientIn atmospheric sciences , the pressure gradient is a physical quantity that describes in which direction and at what rate the pressure changes the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pressure per unit length...