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{{Sound measurements}}
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'''Particle displacement''' or '''displacement amplitude''' (represented in [[mathematics]] by the [[Lower case|lower-case]] [[Greek alphabet#Main table|Greek letter]] [[Xi (letter)|&xi;]]) is a [[measurement]] of [[distance]] of the movement of a particle from its equilibrium position in a medium as it transmits a [[wave]].<ref>
{{cite book
| title = Microsensors, MEMS, and Smart Devices
| author = Julian W. Gardner, V. K. Varadan, Osama O. Awadelkarim
| publisher = John Wiley and Sons
| year = 2001
| isbn = 978-0-471-86109-6
| pages = 321–322
| url = http://books.google.com/books?id=ht69jE9ypSwC&pg=PA321
}}</ref> 
In most cases this is a [[longitudinal wave]] of pressure (such as [[sound]]), but it can also be a [[transverse wave]], such as the [[oscillation|vibration]] of a taut string.  In the case of a [[sound wave]] travelling through [[air]], the '''particle displacement''' is evident in the [[oscillation]]s of air [[molecule]]s with, and against, the direction in which the sound wave is travelling.<ref>{{cite book
| author= Arthur Schuster
| title=An Introduction to the Theory of Optics
| publisher=London: Edward Arnold
| year=1904
| url = http://books.google.com/books?id=Zb4KAAAAIAAJ&printsec=frontcover&dq=An+Introduction+to+the+Theory+of+Optics+By+Arthur+Schuster
}} </ref> 
A particle of the medium undergoes displacement according to the [[particle velocity]] of the wave traveling through the medium, while the sound wave itself moves at the [[speed of sound]], equal to 343&nbsp;m/s in air at 20 °C.
 
The instantaneous particle displacement ''ξ'' for a wave is:<ref>
{{cite book
  | author = John Eargle
  | authorlink = John M. Eargle
  | title = The Microphone Book: From mono to stereo to surround – a guide to microphone design and application  | publisher = Focal Press  | date = January 2005
  | location = Burlington, Ma  | pages = 27
  | url =http://books.google.com/books?id=w8kXMVKOsY0C&pg=PA27&dq=instantaneous+particle+displacement
  | isbn =978-0-240-51961-6
}}</ref>
 
:<math>
\xi = \int_{t} v\, \mathrm{d}t
</math>
 
If the wave is a standing wave or a traveling wave containing a single frequency, the particle displacement is:
:<math>
\xi = \frac{1}{Z} \int_{t} p\, \mathrm{d}t
</math>
This expression for <math>\xi</math> undergoes simple harmonic oscillation, and as such is usually expressed as an [[root mean square|RMS]] time average.
 
'''Particle displacement''' for a traveling wave containing a single frequency can be represented in terms of other measurements:
:<math>
\xi = \frac{v}{\omega}
    = \frac{p}{Z_0 \cdot \omega}
    = \frac{a}{\omega^2}
    = \frac{1}{\omega}\sqrt{\frac{I}{Z_0}}
    = \frac{1}{\omega}\sqrt{\frac{E}{\rho}}
    = \frac{1}{\omega}\sqrt{\frac{P_{ac}}{Z_0 \cdot A}}
</math>
where in the above equation, the quantities <math>\xi, v, a, I, E, P_{ac}</math> 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, <math>Z=Z_0</math>. Further representations for <math>\xi</math> can be found from the above equations using the replacement <math>\omega=2\pi{f}</math>.
 
{| class="wikitable"
! Symbol !! Units !! Meaning
|-
! ''ξ''
| m, meters || Particle displacement
|-
! ''v''
| [[Meters per second|m/s]] || [[particle velocity]]
|-
! ω = 2π''f''
| [[radian]]s/[[second|s]] || [[angular frequency]]
|-
! ''f''
| Hz, [[hertz]] || [[frequency]]
|-
! ''p''
| Pa, [[pascal (unit)|pascal]]s || [[sound pressure]]
|-
! ''Z<sub>0</sub>'' = ''c'' · ''ρ''
| [[Newton (unit)|N]]·[[second|s]]/m<sup>3</sup> || [[characteristic impedance]]
|-
! ''Z'' = ''p'' / ''v''
| [[Newton (unit)|N]]·[[second|s]]/m<sup>3</sup> || [[acoustic impedance]]
|-
! ''c''
| m/[[second|s]] || [[Speed of sound]]
|-
! ''ρ''
| [[Kilogram|kg]]/m<sup>3</sup> || [[Density of air]]
|-
! ''I''
| [[Watt|W]]/m<sup>2</sup> || [[sound intensity]]
|-
! ''E''
| [[Watt|W]]·[[second|s]]/m<sup>3</sup> || [[sound energy density]]
|-
! ''P''<sub>ac</sub>
| W, [[watt]]s || [[sound power]] or [[acoustic power]]
|-
! ''A''
| m<sup>2</sup> || [[Area]]
|-
! ''a''
| m/[[second|s]]<sup>2</sup> || [[Particle acceleration]]
|}
 
== See also ==
 
* [[Wave]]
* [[Sound particle]]
 
==References and notes==
{{reflist}}
 
'''Related Reading:'''
*{{cite book  | author=Wood, Robert Williams
| title=Physical optics  | publisher=New York: The Macmillan Company | year=1914}}
*{{cite book  | author=Strong, John Donovan; and Hayward, Roger
| title=Concepts of Classical Optics  | publisher=Dover Publications | year=January 2004
| isbn= 978-0-486-43262-5 | page= }}
*{{cite book  | last = Barron  | first = Randall F.
  | authorlink =  | coauthors =    | title = Industrial noise control and acoustics
  | publisher = CRC Press  | date = January 2003
  | location = NYC, New York  | pages = 79, 82, 83, 87
  | url =http://books.google.com/books?id=k1tXPl2hC-cC&pg=PA82&dq=instantaneous+particle+displacement
  | doi =  | id =
  | isbn =978-0-8247-0701-9}}
 
== External links ==
*[http://acoustics.open.ac.uk/802574C70048F266/%28httpAssets%29/EC0466002A53AFDD802574E200381B0C/$file/ali_tonddast_navaei_thesis.pdf Acoustic particle-image velocimetry - Development and applications]
*[http://www.sengpielaudio.com/calculator-ak-ohm.htm Ohm's law as acoustic equivalent  - calculations]
*[http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf]
 
[[Category:Sound measurements]]

Latest revision as of 19:25, 1 January 2015

Would you like an athletic shoe created by a firm that assumes that a superstar athlete staying compensated tens of millions for an endorsement can market you anything, or a shoe made by a corporation that thinks in better fit and far better technological know-how as a way to get paid your business?

If you want the advertising and marketing method, you look to be in the bulk. If you desire superior healthy and technologies to much more hoopla, there is a excellent chance that you get New Stability athletic shoes.
I was vaguely conscious of New Equilibrium shoes when I was told that I must be wearing B width shoes instead than the D width footwear I experienced been buying all of my lifetime. The future time I purchased athletic footwear, I discovered that New Equilibrium appears to be one of the number of sneaker companies offering their products in slender dimensions. New Balance shoes are generally available in a range of widths from B or D to 4E, but some products are made available in widths of up to 6E.
When shoe giant Nike, with about 10 occasions the annual revenue of New Harmony, has created its status on the endorsements of athletes this kind of as Michael Jordan and Bo Jackson, New Harmony originally created its standing on word-of-mouth or regional sporting activities fairs, and has considering that adopted the slogan ndorsed by No A single?to reflect the reality that New Equilibrium currently has no paid out endorsements by athletes.

In 1906, William J. Riley founded the New Harmony Arch Assist Business to manufacture arch supports and other extras to enhance shoe match. In 1934, major New Harmony salesman Arthur Corridor turned Riley husband or wife. Corridor had been incredibly thriving advertising the business products to people whose jobs expected them to spend a ton of time on their ft.
In 1961, right after Corridor son-in-legislation and daughter had taken over the firm, New Stability introduced the world to start with jogging shoe created with a ripple sole, which was also the very first running shoe out there in many widths. That shoe, referred to as the rackster,?became popular amid jogging coaches and led to a escalating track record for New Balance in producing modern and specialized footwear.

In 1972, Jim Davis bought New Harmony, which at the time consisted of half a dozen people making thirty pairs of footwear per working day. Davis timing turned out to be perfect, as running took the U.S. by storm in the seventies. In 1975, Tom Fleming gained the New York Metropolis Marathon in a pair of New Harmony sneakers.
Davis spouse Anne joined the firm in 1978 and they expanded New Equilibrium into a global corporation. In the exact same 12 months, the similar model New Balance shoe as worn by Tom Fleming was named the amount one functioning shoe by Runner World journal. This assisted to reaffirm the organization popularity amid really serious athletes.

In 1985, New Stability attempted to contend with Nike for the basketball shoe industry by signing basketball star James Worthy and adding his name to a line of sneakers. Having said that, New Harmony experienced a difficult time in the basketball shoe industry, foremost them to fall all output of such sneakers. This also led New Equilibrium back again to its prosperous marketing campaign of concentrating on producing fantastic shoes, and to the adoption of the slogan that helps make up the title of this write-up.

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