Boundary-value analysis - Revision history

en>Chadernook: /* Application */ - Fixed LaTeX formatting, should not really be italics

2014-10-22T16:45:09Z

Application: - Fixed LaTeX formatting, should not really be italics

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	~~{{about\|small-scale particle acceleration in [[acoustics]]\|acceleration of charged particles to very high energies\|particle accelerator}}~~		My name is Zachery and I am studying Biological Sciences and International Relations at Krefeld / Germany.<br><br>my web site: [http://www.greatlakespsychologygroup.com/services/marriage-counseling.html Fifa 15 Coin Generator]
	~~{{multiple issues\|~~
	~~{{Notability\|date=October 2008}}~~
	~~{{Unreferenced\|date=October 2008}}~~
	}}

	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\|metre/second²]]. In [[acoustics]] or [[physics]], '''acceleration''' (symbol: ''a'') is ~~defined as the rate of change (or time [[derivative]]) of [[velocity]]. It is thus a [[vector (geometric)\|vector]] quantity with dimension [[length]]/[[time]]². In [[SI\|SI units]], this is m/s².~~

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

	~~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:~~
	~~:<math>~~
	~~\mathbf{\bar{a}} = {\mathbf{v} - \mathbf{u} \over t}~~
	~~</math>~~

	~~where~~
	~~:<math>\mathbf{\bar{a}}</math> is the average acceleration (m/s²)~~

	~~<math>\mathbf{u}</math> is the initial velocity (m/s)~~

	~~<math>\mathbf{v}</math> is the final velocity (m/s)~~

	~~<math>t</math> is the time interval (s)~~

	~~[[:wikt:transverse\|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~~
	~~:<math> \mathbf{a} = - \frac{v^2}{r} \frac{\mathbf{r}}{r} = - \omega^2 \mathbf{r}<~~/~~math>~~

	~~One common unit of acceleration is ''[[g-force]]'', one ''g'' being the acceleration caused by the [[standard gravity\|gravity of Earth]]~~.

	~~In [[classical mechanics]], acceleration <math> a \ </math> is related to [[Force (physics)\|force]] <math>F \ </math> and [[mass]]~~ <~~math~~>~~m \~~ <~~/math~~> ~~(assumed to be constant) by way of [[Newton's laws of motion\|Newton's second law]]:~~
	:~~<math>~~
	~~F = m \cdot a~~
	~~</math>~~

	~~== Equations in terms of other measurements ==~~
	~~The '''Particle acceleration''' of the air particles ''a'' in m/s² of a plain sound wave is:~~
	~~:<math>~~
	~~a = \xi \cdot \omega^2 = v \cdot \omega = \frac{p \cdot \omega}{Z} = \omega \sqrt \frac{J}{Z} = \omega \sqrt \frac{E}{\rho} = \omega \sqrt \frac{P_{ac}}{Z \cdot A}~~
	~~</math>~~

	~~{\|border="1" cellpadding="0" cellspacing="0"~~
	~~! Symbol !! Units !! Meaning~~
	\|-
	~~! ''a''~~
	~~\| m/[[second\|s]]² \|\| particle acceleration~~
	\|-
	~~! ''v''~~
	~~\| [[Meters per second\|m/s]] \|\| [[particle velocity]]~~
	\|-
	~~! ''ξ''~~
	~~\| m, meters \|\| [[particle displacement]]~~
	\|-
	~~! ''<math>\omega</math>'' = 2 · <math>\pi</math> · ''f''~~
	~~\| [[radian]]s/[[second\|s]] \|\| [[angular frequency]]~~
	\|-
	~~! ''f''~~
	~~\| Hz, [[hertz]] \|\| [[frequency]]~~
	\|-
	~~! ''p''~~
	~~\| Pa, [[pascal (unit)\|pascal]]s \|\| [[sound pressure]]~~
	\|-
	~~! ''Z''~~
	~~\| [[newton (unit)\|N]]·[[second\|s]]/m³ \|\| [[acoustic impedance]]~~
	\|-
	~~! ''J''~~
	~~\| [[Watt\|W]]/m² \|\| [[sound intensity]]~~
	\|-
	~~! ''E''~~
	~~\| [[Watt\|W]]·[[second\|s]]/m³ \|\| [[sound energy density]]~~
	\|-
	~~! ''P''<sub>ac</sub>~~
	~~\| W, [[watt]]s \|\| [[sound power]] or [[acoustic power]]~~
	\|-
	~~! ''A''~~
	~~\| m² \|\| [[area]]~~
	\|}

	~~==See also==~~

	* [[Sound pressure]]
	* [[Particle displacement]]
	* [[Particle velocity]]

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

	~~[[Category:Acoustics]]~~

	~~[[de:Schallbeschleunigung]~~]

en>Mojdadyr: /* Formal Definition */

2013-10-08T13:26:00Z

Formal Definition

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en>Nmondal at 10:50, 2 July 2012

2012-07-02T10:50:28Z

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