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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|
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| {{Notability|date=October 2008}}
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| {{Unreferenced|date=October 2008}}
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| }}
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| 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.
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| 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
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| :<math>
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| \mathbf{a} = {d\mathbf{v}\over dt}
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| </math>
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| where
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| *''a'' is the acceleration vector
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| *''v'' is the velocity vector expressed in m/s
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| *''t'' is time expressed in seconds.
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| 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").
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| An alternative equation is:
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| :<math>
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| \mathbf{\bar{a}} = {\mathbf{v} - \mathbf{u} \over t}
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| </math>
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| where
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| :<math>\mathbf{\bar{a}}</math> is the average acceleration (m/s²)
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| <math>\mathbf{u}</math> is the initial velocity (m/s)
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| <math>\mathbf{v}</math> is the final velocity (m/s)
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| <math>t</math> is the time interval (s)
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| [[: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
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| :<math> \mathbf{a} = - \frac{v^2}{r} \frac{\mathbf{r}}{r} = - \omega^2 \mathbf{r}</math>
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| One common unit of acceleration is ''[[g-force]]'', one ''g'' being the acceleration caused by the [[standard gravity|gravity of Earth]].
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| 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]]:
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| :<math> | |
| F = m \cdot a
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| </math>
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| == Equations in terms of other measurements ==
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| The '''Particle acceleration''' of the air particles ''a'' in m/s² of a plain sound wave is:
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| :<math>
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| 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}
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| </math>
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| {|border="1" cellpadding="0" cellspacing="0"
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| ! Symbol !! Units !! Meaning
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| |-
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| ! ''a''
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| | m/[[second|s]]² || particle acceleration
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| |-
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| ! ''v''
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| | [[Meters per second|m/s]] || [[particle velocity]]
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| |-
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| ! ''ξ''
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| | m, meters || [[particle displacement]]
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| |-
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| ! ''<math>\omega</math>'' = 2 · <math>\pi</math> · ''f''
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| | [[radian]]s/[[second|s]] || [[angular frequency]]
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| |-
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| ! ''f''
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| | Hz, [[hertz]] || [[frequency]]
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| |-
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| ! ''p''
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| | Pa, [[pascal (unit)|pascal]]s || [[sound pressure]]
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| |-
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| ! ''Z''
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| | [[newton (unit)|N]]·[[second|s]]/m³ || [[acoustic impedance]]
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| |-
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| ! ''J''
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| | [[Watt|W]]/m² || [[sound intensity]]
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| |-
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| ! ''E''
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| | [[Watt|W]]·[[second|s]]/m³ || [[sound energy density]]
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| |-
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| ! ''P''<sub>ac</sub>
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| | W, [[watt]]s || [[sound power]] or [[acoustic power]]
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| |-
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| ! ''A''
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| | m² || [[area]]
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| |}
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| ==See also==
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| * [[Sound pressure]]
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| * [[Particle displacement]]
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| * [[Particle velocity]]
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| == External links ==
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| *[http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf]
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| [[Category:Acoustics]]
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| [[de:Schallbeschleunigung]]
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My name is Zachery and I am studying Biological Sciences and International Relations at Krefeld / Germany.
my web site: Fifa 15 Coin Generator