Editing Speed of sound (section)

====Seawater====
{{See also|Sound speed profile}}
[[File:Underwater speed of sound.svg|thumb|Speed of sound as a function of depth at a position north of Hawaii in the [[Pacific Ocean]] derived from the 2005 [[World Ocean Atlas]]. The [[SOFAR channel]] spans the minimum in the speed of sound at about 750 m depth.]]

In salt water that is free of air bubbles or suspended sediment, sound travels at about {{val|1500|u=m/s}} ({{val|1500.235|u=m/s}} at {{val|1000|ul=kilopascals}}, {{val|10|u=degC}} and 3% [[salinity]] by one method).<ref>{{cite journal|last1=Wong|first1=George S. K.|last2=Zhu|first2=Shi-ming|title=Speed of sound in seawater as a function of salinity, temperature, and pressure|journal=The Journal of the Acoustical Society of America | date=1995 | volume=97 | issue=3|page=1732|doi=10.1121/1.413048|bibcode=1995ASAJ...97.1732W}}</ref> The speed of sound in seawater depends on pressure (hence depth), temperature (a change of {{val|1|u=degC}} ~ {{val|4|u=m/s}}), and [[salinity]] (a change of 1[[Per mil|‰]] ~ {{val|1|u=m/s}}), and empirical equations have been derived to accurately calculate the speed of sound from these variables.<ref>[http://webarchive.loc.gov/all/20030402194852/http://handle.dtic.mil/100.2/ADB199453 APL-UW TR 9407 High-Frequency Ocean Environmental Acoustic Models Handbook], pp. I1-I2.</ref><ref>{{cite web |last1=Robinson|first1=Stephen |title=Technical Guides – Speed of Sound in Sea-Water|url=http://resource.npl.co.uk/acoustics/techguides/soundseawater/content.html |website=National Physical Laboratory|access-date=7 December 2016|date=22 September 2005 | archive-date=29 April 2017|archive-url=https://web.archive.org/web/20170429192345/http://resource.npl.co.uk/acoustics/techguides/soundseawater/content.html|url-status=dead}}</ref> Other factors affecting the speed of sound are minor. Since in most ocean regions temperature decreases with depth, the profile of the speed of sound with depth decreases to a minimum at a depth of several hundred metres. Below the minimum, sound speed increases again, as the effect of increasing pressure overcomes the effect of decreasing temperature (right).<ref>{{cite web
| url = http://www.dosits.org/science/soundmovement/speedofsound/
| title = How Fast Does Sound Travel?
| work = Discovery of Sound in the Sea
| publisher = University of Rhode Island
| access-date = 30 November 2010
| archive-date = 20 May 2017
| archive-url = https://web.archive.org/web/20170520205400/http://www.dosits.org/science/soundmovement/speedofsound/
| url-status = dead
}}</ref> For more information see Dushaw et al.<ref name=Dushaw93/>

An empirical equation for the speed of sound in sea water is provided by Mackenzie:<ref>{{cite journal
| last = Kenneth V.
| first = Mackenzie
| title = Discussion of sea-water sound-speed determinations
| year = 1981
| journal = Journal of the Acoustical Society of America
| volume = 70
| issue = 3
| pages = 801–806
| doi = 10.1121/1.386919
|bibcode = 1981ASAJ...70..801M}}</ref>
<math display="block">c(T, S, z) = a_1 + a_2 T + a_3 T^2 + a_4 T^3 + a_5 (S - 35) + a_6 z + a_7 z^2 + a_8 T(S - 35) + a_9 T z^3,</math>
where
* ''T'' is the temperature in degrees Celsius;
* ''S'' is the salinity in parts per thousand;
* ''z'' is the depth in metres.

The constants ''a''<sub>1</sub>, ''a''<sub>2</sub>, ..., ''a''<sub>9</sub> are
<math display="block">\begin{align}
a_1 &= 1,448.96,             & a_2 &= 4.591,                 & a_3 &= -5.304 \times 10^{-2},\\
a_4 &= 2.374 \times 10^{-4}, & a_5 &= 1.340,                 & a_6 &= 1.630 \times 10^{-2},\\
a_7 &= 1.675 \times 10^{-7}, & a_8 &= -1.025 \times 10^{-2}, & a_9 &= -7.139 \times 10^{-13},
\end{align}</math>
with check value {{val|1550.744|u=m/s}} for {{math|1=''T'' = {{val|25|u=degC}}}}, {{nobreak|1=''S'' = 35 parts per thousand}}, {{nobreak|1=''z'' = 1,000 m}}. This equation has a standard error of {{val|0.070|u=m/s}} for salinity between 25 and 40 [[Parts per thousand|ppt]]. See [http://resource.npl.co.uk/acoustics/techguides/soundseawater/] for an online calculator.

(The Sound Speed vs. Depth graph does ''not'' correlate directly to the MacKenzie formula.
This is due to the fact that the temperature and salinity varies at different depths.
When ''T'' and ''S'' are held constant, the formula itself is always increasing with depth.)

Other equations for the speed of sound in sea water are accurate over a wide range of conditions, but are far more complicated, e.g., that by V. A. Del Grosso<ref>{{cite journal
| last = Del Grosso
| first = V. A.
| title = New equation for speed of sound in natural waters (with comparisons to other equations)
| year = 1974
| journal = Journal of the Acoustical Society of America
| volume = 56
| issue = 4
| pages = 1084–1091
| doi = 10.1121/1.1903388 | bibcode = 1974ASAJ...56.1084D| doi-access = free
}}</ref> and the Chen-Millero-Li Equation.<ref name=Dushaw93>{{cite journal
| last1 = Dushaw
| first1 = Brian D.
| last2 = Worcester
| first2 = P. F.
| last3 = Cornuelle
| first3 = B. D.
| last4 = Howe
| first4 = B. M.
| title = On Equations for the Speed of Sound in Seawater
| year = 1993
| journal = Journal of the Acoustical Society of America
| volume = 93
| issue = 1
| pages = 255–275
| doi = 10.1121/1.405660|bibcode = 1993ASAJ...93..255D}}</ref><ref>{{cite journal
| last1 = Meinen
| first1 = Christopher S.
| last2 = Watts
| first2 = D. Randolph
| title = Further Evidence that the Sound-Speed Algorithm of Del Grosso Is More Accurate Than that of Chen and Millero
| year = 1997
| journal = Journal of the Acoustical Society of America
| volume = 102
| issue = 4
| pages = 2058–2062
| doi = 10.1121/1.419655|bibcode = 1997ASAJ..102.2058M
| s2cid = 38144335
| url = https://digitalcommons.uri.edu/cgi/viewcontent.cgi?article=1249&context=gsofacpubs
| url-access = subscription
}}</ref>