# 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/second&sup2;. In acoustics or physics, acceleration (symbol: "a") is defined as the rate of change (or time derivative) of velocity. It is thus a vector quantity with dimension length/time². In SI units, this is m/s².

To accelerate an object (air particle) is to change its velocity over a period of time. Acceleration is defined technically as "the rate of change of velocity of an object with respect to time" and is given by the equation :$mathbf\left\{a\right\} = \left\{dmathbf\left\{v\right\}over dt\right\}$

where
*"a" is the acceleration vector
*"v" is the velocity vector expressed in m/s
*"t" is time expressed in seconds.

This equation gives "a" the units of m/(s·s), or m/s² (read as "metres per second per second", or "metres per second squared").

An alternative equation is::

where : is the average acceleration (m/s&sup2;)

$mathbf\left\{u\right\}$ is the initial velocity (m/s)

$mathbf\left\{v\right\}$ is the final velocity (m/s)

$t$ is the time interval (s)

Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get a circular motion. For this centripetal acceleration we have:$mathbf\left\{a\right\} = - frac\left\{v^2\right\}\left\{r\right\} frac\left\{mathbf\left\{r\left\{r\right\} = - omega^2 mathbf\left\{r\right\}$

One common unit of acceleration is "g-force", one "g" being the acceleration caused by the gravity of Earth.

In classical mechanics, acceleration $a$ is related to force $F$ and mass $m$ (assumed to be constant) by way of Newton's second law: :$F = m cdot a$

Equations in terms of other measurements

The Particle acceleration of the air particles "a" in m/s² of a plain sound wave is::$a = xi cdot omega^2 = v cdot omega = frac\left\{p cdot omega\right\}\left\{Z\right\} = omega sqrt frac\left\{J\right\}\left\{Z\right\} = omega sqrt frac\left\{E\right\}\left\{ ho\right\} = omega sqrt frac\left\{P_\left\{ak\left\{Z cdot A\right\}$

ee also

* Sound pressure
* Particle displacement
* Particle velocity

* [http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf]

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• instantaneous sound particle acceleration — akimirkinis garsinis dalelių pagreitis statusas T sritis Standartizacija ir metrologija apibrėžtis Dydis, lygus akimirkinio garsinio terpės dalelių greičio pokyčiui per vienetinį laiko tarpą, t. y. a = δu/δt; čia δu – dalelių greičio pokytis, δt… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

• 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… …   Wikipedia

• particle accelerator — accelerator (def. 7). [1945 50] * * * Device that accelerates a beam of fast moving, electrically charged atoms (ions) or subatomic particles. Accelerators are used to study the structure of atomic nuclei (see atom) and the nature of subatomic… …   Universalium

• Particle accelerator — Atom smasher redirects here. For other uses, see Atom smasher (disambiguation). A 1960s single stage 2 MeV linear Van de Graaff accelerator, here opened for maintenance A particle accelerator is a device that uses electromagnetic fields to… …   Wikipedia

• Acceleration — Accelerate redirects here. For other uses, see Accelerate (disambiguation). Classical mechanics Newton s Second Law …   Wikipedia

• Particle beam weapon — A particle beam weapon uses an ultra high energy beam of atoms or electrons (i.e., a particle beam) to damage a material target by hitting it, and thus disrupting its atomic and molecular structure. A particle beam weapon is a type of directed… …   Wikipedia

• Particle-in-cell — The Particle in Cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in a Lagrangian frame are tracked in continuous phase space, whereas …   Wikipedia

• acceleration — 1. The act of accelerating. 2. The rate of increase in velocity per unit of time; commonly expressed in g units; also expressed in centimeters or feet per second squared. 3. The rate of increasing deviation from a rectilinear course. See radial a …   Medical dictionary

• Plasma acceleration — is a technique for accelerating charged particles, such as electrons, positrons and ions, using an electric field associated with an electron plasma wave. The wave is created by the passage of a very brief laser or electron pulse through the… …   Wikipedia

• Multiphase particle-in-cell method — The multiphase particle in cell method (MP PIC) is a numerical method for modeling particle fluid and particle particle interactions in a computational fluid dynamics (CFD) calculation. The MP PIC method achieves greater stability than its… …   Wikipedia