The speed of sound is the distance travelled per unit of time by a

_{s}'' is a coefficient of stiffness, the isentropic _{2} which ''is'' a dispersive medium, and causes dispersion to air at

density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematica ...

(also proportional to pressure) have equal but opposite effects on the speed of sound, and the two contributions cancel out exactly. In a similar way, compression waves in solids depend both on compressibility and density—just as in liquids—but in gases the density contributes to the compressibility in such a way that some part of each attribute factors out, leaving only a dependence on temperature, molecular weight, and heat capacity ratio which can be independently derived from temperature and molecular composition (see derivations below). Thus, for a single given gas (assuming the molecular weight does not change) and over a small temperature range (for which the heat capacity is relatively constant), the speed of sound becomes dependent on only the temperature of the gas.
In non-ideal gas behavior regimen, for which the Van der Waals gas equation would be used, the proportionality is not exact, and there is a slight dependence of sound velocity on the gas pressure.
Humidity has a small but measurable effect on the speed of sound (causing it to increase by about 0.1%–0.6%), because

density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematica ...

.
Using the _{ideal} is the speed of sound in an ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...

;
* ''R'' is the molar gas constant;
* ''k'' is the _{air} have been found to vary slightly from experimentally determined values.U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976.
Newton famously considered the speed of sound before most of the development of

_{0} is (= ), giving a theoretical value of (= = = = ). Values ranging from 331.3 to 331.6 m/s may be found in reference literature, however;
* ''T''_{20} is (= = ), giving a value of (= = = = );
* ''T''_{25} is (= = ), giving a value of (= = = = ).
In fact, assuming an ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...

, the speed of sound ''c'' depends on temperature and composition only, not on the pressure or density (since these change in lockstep for a given temperature and cancel out). Air is almost an ideal gas. The temperature of the air varies with altitude, giving the following variations in the speed of sound using the standard atmosphere—''actual conditions may vary''.
Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:

shear modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:
:G \ \stack ...

of the elastic materials;
* ''E'' is the _{solid,p} of . This is in reasonable agreement with ''c''_{solid,p} measured experimentally at for a (possibly different) type of steel. The shear speed ''c''_{solid,s} is estimated at using the same numbers.
Speed of sound in semiconductor solids can be very sensitive to the amount of electronic dopant in them.

shear modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:
:G \ \stack ...

. This speed of sound for pressure waves in long rods will always be slightly less than the same speed in homogeneous 3-dimensional solids, and the ratio of the speeds in the two different types of objects depends on Poisson's ratio for the material.

bulk modulus
The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume.
Other moduli describe ...

of the fluid.

_{1}, ''a''_{2}, ..., ''a''_{9} are
: $\backslash begin\; a\_1\; \&=\; 1,448.96,\; \&a\_2\; \&=\; 4.591,\; \&a\_3\; \&=\; -5.304\; \backslash times\; 10^,\backslash \backslash \; a\_4\; \&=\; 2.374\; \backslash times\; 10^,\; \&a\_5\; \&=\; 1.340,\; \&a\_6\; \&=\; 1.630\; \backslash times\; 10^,\backslash \backslash \; a\_7\; \&=\; 1.675\; \backslash times\; 10^,\; \&a\_8\; \&=\; -1.025\; \backslash times\; 10^,\; \&a\_9\; \&=\; -7.139\; \backslash times\; 10^,\; \backslash end$
with check value for , , . This equation has a standard error of for salinity between 25 and 40 ppt. Se

for an online calculator. (Note: 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 and the Chen-Millero-Li Equation.

_{i} is the _{e} is the

Speed of Sound Calculator

Speed of sound: Temperature Matters, Not Air Pressure

How to Measure the Speed of Sound in a Laboratory

* ttp://www.dosits.org/ Discovery of Sound in the Sea(uses of sound by humans and other animals) {{Authority control Fluid dynamics Aerodynamics Acoustics Sound Sound measurements Physical quantities Chemical properties Velocity Temporal rates

sound wave
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by th ...

as it propagates through an elastic
Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics.
Elastic may also refer to:
Alternative name
* Rubber band, ring-shaped band of rubber used to hold objects togethe ...

medium. At , the speed of sound in air is about , or one kilometre
The kilometre ( SI symbol: km; or ), spelt kilometer in American English, is a unit of length in the International System of Units (SI), equal to one thousand metres ( kilo- being the SI prefix for ). It is now the measurement unit used for e ...

in or one mile
The mile, sometimes the international mile or statute mile to distinguish it from other miles, is a British imperial unit and United States customary unit of distance; both are based on the older English unit of length equal to 5,280 Englis ...

in . It depends strongly on temperature as well as the medium through which a sound wave
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by th ...

is propagating. At , the speed of sound in air is about .
The speed of sound in an ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...

depends only on its temperature and composition. The speed has a weak dependence on frequency and pressure in ordinary air, deviating slightly from ideal behavior.
In colloquial speech, ''speed of sound'' refers to the speed of sound waves in air
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...

. However, the speed of sound varies from substance to substance: typically, sound travels most slowly in gases, faster in liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas ...

s, and fastest in solids
Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural ...

. For example, while sound travels at in air, it travels at in water
Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...

(almost 4.3 times as fast) and at in iron
Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...

(almost 15 times as fast). In an exceptionally stiff material such as diamond, sound travels at , about 35 times its speed in air and about the fastest it can travel under normal conditions.
Sound waves in solids are composed of compression waves (just as in gases and liquids), and a different type of sound wave called a shear wave, which occurs only in solids. Shear waves in solids usually travel at different speeds than compression waves, as exhibited in seismology
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...

. The speed of compression waves in solids is determined by the medium's compressibility, shear modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:
:G \ \stack ...

and density. The speed of shear waves is determined only by the solid material's shear modulus and density.
In fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) ...

, the speed of sound in a fluid medium (gas or liquid) is used as a relative measure for the speed of an object moving through the medium. The ratio of the speed of an object to the speed of sound (in the same medium) is called the object's Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \fra ...

. Objects moving at speeds greater than the speed of sound (') are said to be traveling at supersonic
Supersonic speed is the speed of an object that exceeds the speed of sound ( Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times ...

speeds.
History

Sir Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the great ...

's 1687 '' Principia'' includes a computation of the speed of sound in air as . This is too low by about 15%. The discrepancy is due primarily to neglecting the (then unknown) effect of rapidly-fluctuating temperature in a sound wave (in modern terms, sound wave compression and expansion of air is an adiabatic process
In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, ...

, not an isothermal process). This error was later rectified by Laplace.
During the 17th century there were several attempts to measure the speed of sound accurately, including attempts by Marin Mersenne
Marin Mersenne, OM (also known as Marinus Mersennus or ''le Père'' Mersenne; ; 8 September 1588 – 1 September 1648) was a French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for ...

in 1630 (1,380 Parisian feet per second), Pierre Gassendi in 1635 (1,473 Parisian feet per second) and Robert Boyle (1,125 Parisian feet per second). In 1709, the Reverend William Derham, Rector of Upminster, published a more accurate measure of the speed of sound, at 1,072 Parisian feet per second. (The Parisian foot was 325 mm. This is longer than the standard "international foot" in common use today, which was officially defined in 1959 as 304.8 mm, making the speed of sound at 1,055 Parisian feet per second).
Derham used a telescope from the tower of the church of St. Laurence, Upminster to observe the flash of a distant shotgun being fired, and then measured the time until he heard the gunshot with a half-second pendulum. Measurements were made of gunshots from a number of local landmarks, including North Ockendon church. The distance was known by triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points.
Applications
In surveying
Specifically in surveying, triangulation involves only angle me ...

, and thus the speed that the sound had travelled was calculated.Basic concepts

The transmission of sound can be illustrated by using a model consisting of an array of spherical objects interconnected by springs. In real material terms, the spheres represent the material's molecules and the springs represent the bonds between them. Sound passes through the system by compressing and expanding the springs, transmitting the acoustic energy to neighboring spheres. This helps transmit the energy in-turn to the neighboring sphere's springs (bonds), and so on. The speed of sound through the model depends on thestiffness
Stiffness is the extent to which an object resists deformation in response to an applied force.
The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.
Calculations
The stiffness, k, of a bo ...

/rigidity of the springs, and the mass of the spheres. As long as the spacing of the spheres remains constant, stiffer springs/bonds transmit energy quicker, while larger spheres transmit the energy slower.
In a real material, the stiffness of the springs is known as the "elastic modulus
An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is ...

", and the mass corresponds to the material density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematica ...

. Given that all other things being equal (ceteris paribus
' (also spelled '; () is a Latin phrase, meaning "other things equal"; some other English translations of the phrase are "all other things being equal", "other things held constant", "all else unchanged", and "all else being equal". A statement ...

), sound will travel slower in spongy materials, and faster in stiffer ones. Effects like dispersion and reflection can also be understood using this model.
For instance, sound will travel 1.59 times faster in nickel than in bronze, due to the greater stiffness of nickel at about the same density. Similarly, sound travels about 1.41 times faster in light hydrogen ( protium) gas than in heavy hydrogen (deuterium
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one ...

) gas, since deuterium has similar properties but twice the density. At the same time, "compression-type" sound will travel faster in solids than in liquids, and faster in liquids than in gases, because the solids are more difficult to compress than liquids, while liquids, in turn, are more difficult to compress than gases.
Some textbooks mistakenly state that the speed of sound increases with density. This notion is illustrated by presenting data for three materials, such as air, water, and steel; they each have vastly different compressibility, which more than makes up for the density differences. An illustrative example of the two effects is that sound travels only 4.3 times faster in water than air, despite enormous differences in compressibility of the two media. The reason is that the larger density of water, which works to ''slow'' sound in water relative to air, nearly makes up for the compressibility differences in the two media.
A practical example can be observed in Edinburgh when the "One o'Clock Gun" is fired at the eastern end of Edinburgh Castle. Standing at the base of the western end of the Castle Rock, the sound of the Gun can be heard through the rock, slightly before it arrives by the air route, partly delayed by the slightly longer route. It is particularly effective if a multi-gun salute such as for "The Queen's Birthday" is being fired.
Compression and shear waves

In a gas or liquid, sound consists of compression waves. In solids, waves propagate as two different types. Alongitudinal wave
Longitudinal waves are waves in which the vibration of the medium is parallel ("along") to the direction the wave travels and displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal waves ...

is associated with compression and decompression in the direction of travel, and is the same process in gases and liquids, with an analogous compression-type wave in solids. Only compression waves are supported in gases and liquids. An additional type of wave, the transverse wave, also called a shear wave, occurs only in solids because only solids support elastic deformations. It is due to elastic deformation of the medium perpendicular to the direction of wave travel; the direction of shear-deformation is called the " polarization" of this type of wave. In general, transverse waves occur as a pair of orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...

polarizations.
These different waves (compression waves and the different polarizations of shear waves) may have different speeds at the same frequency. Therefore, they arrive at an observer at different times, an extreme example being an earthquake
An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, from ...

, where sharp compression waves arrive first and rocking transverse waves seconds later.
The speed of a compression wave in a fluid is determined by the medium's compressibility and density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematica ...

. In solids, the compression waves are analogous to those in fluids, depending on compressibility and density, but with the additional factor of shear modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:
:G \ \stack ...

which affects compression waves due to off-axis elastic energies which are able to influence effective tension and relaxation in a compression. The speed of shear waves, which can occur only in solids, is determined simply by the solid material's shear modulus and density.
Equations

The speed of sound in mathematical notation is conventionally represented by ''c'', from the Latin ''celeritas'' meaning "velocity". For fluids in general, the speed of sound ''c'' is given by the Newton–Laplace equation: : $c\; =\; \backslash sqrt,$ where * ''Kbulk modulus
The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume.
Other moduli describe ...

(or the modulus of bulk elasticity for gases);
* $\backslash rho$ is the density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematica ...

.
Thus, the speed of sound increases with the stiffness (the resistance of an elastic body to deformation by an applied force) of the material and decreases with an increase in density. For ideal gases, the bulk modulus ''K'' is simply the gas pressure multiplied by the dimensionless adiabatic index, which is about 1.4 for air under normal conditions of pressure and temperature.
For general equations of state, if classical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mech ...

is used, the speed of sound ''c'' can be derived as follows:
Consider the sound wave propagating at speed $v$ through a pipe aligned with the $x$ axis and with a cross-sectional area of $A$. In time interval $dt$ it moves length $dx\; =\; v\; \backslash ,\; dt$. In steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p ...

, the mass flow rate $\backslash dot\; m\; =\; \backslash rho\; v\; A$ must be the same at the two ends of the tube, therefore the mass flux
In physics and engineering, mass flux is the rate of mass flow. Its SI units are kg m−2 s−1. The common symbols are ''j'', ''J'', ''q'', ''Q'', ''φ'', or Φ (Greek lower or capital Phi), sometimes with subscript ''m'' to indicate mass is the ...

$j=\backslash rho\; v$ is constant and $v\; \backslash ,\; d\backslash rho\; =\; -\backslash rho\; \backslash ,\; dv$. Per Newton's second law
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in motio ...

, the pressure-gradient force provides the acceleration:
:$\backslash begin\; \backslash frac\; \&=-\backslash frac\backslash frac\backslash \backslash \; \backslash rightarrow\; dP\&=(-\backslash rho\; \backslash ,dv)\backslash frac=(v\; \backslash ,\; d\backslash rho)v\backslash \backslash \; \backslash rightarrow\; v^2\&\; \backslash equiv\; c^2=\backslash frac\; \backslash end$
And therefore:
:$c\; =\; \backslash sqrt,$
where
* ''P'' is the pressure;
* $\backslash rho$ is the density and the derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...

is taken isentropically, that is, at constant entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...

''s''. This is because a sound wave travels so fast that its propagation can be approximated as an adiabatic process
In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, ...

.
If relativistic effects are important, the speed of sound is calculated from the relativistic Euler equations.
In a non-dispersive medium, the speed of sound is independent of sound frequency, so the speeds of energy transport and sound propagation are the same for all frequencies. Air, a mixture of oxygen and nitrogen, constitutes a non-dispersive medium. However, air does contain a small amount of COultrasonic
Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies fr ...

frequencies ().
In a dispersive medium, the speed of sound is a function of sound frequency, through the dispersion relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the ...

. Each frequency component propagates at its own speed, called the phase velocity
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...

, while the energy of the disturbance propagates at the group velocity
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope'' of the wave—propagates through space.
For example, if a stone is thrown into the middl ...

. The same phenomenon occurs with light waves; see optical dispersion for a description.
Dependence on the properties of the medium

The speed of sound is variable and depends on the properties of the substance through which the wave is travelling. In solids, the speed of transverse (or shear) waves depends on the shear deformation under shear stress (called theshear modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:
:G \ \stack ...

), and the density of the medium. Longitudinal (or compression) waves in solids depend on the same two factors with the addition of a dependence on compressibility.
In fluids, only the medium's compressibility and density are the important factors, since fluids do not transmit shear stresses. In heterogeneous fluids, such as a liquid filled with gas bubbles, the density of the liquid and the compressibility of the gas affect the speed of sound in an additive manner, as demonstrated in the hot chocolate effect.
In gases, adiabatic compressibility is directly related to pressure through the heat capacity ratio
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant vol ...

(adiabatic index), while pressure and density are inversely related to the temperature and molecular weight, thus making only the completely independent properties of ''temperature and molecular structure'' important (heat capacity ratio may be determined by temperature and molecular structure, but simple molecular weight is not sufficient to determine it).
Sound propagates faster in low molecular weight
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...

gases such as helium
Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table ...

than it does in heavier gases such as xenon
Xenon is a chemical element with the symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as th ...

. For monatomic gases, the speed of sound is about 75% of the mean speed that the atoms move in that gas.
For a given ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...

the molecular composition is fixed, and thus the speed of sound depends only on its temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...

. At a constant temperature, the gas pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and ...

has no effect on the speed of sound, since the density will increase, and since pressure and oxygen
Oxygen is the chemical element with the chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen Group (periodic table), group in the periodic table, a highly Chemical reaction, reactive nonmetal, and an oxidizing a ...

and nitrogen
Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at seven ...

molecules of the air are replaced by lighter molecules of water
Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...

. This is a simple mixing effect.
Altitude variation and implications for atmospheric acoustics

In theEarth's atmosphere
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...

, the chief factor affecting the speed of sound is the temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...

. For a given ideal gas with constant heat capacity and composition, the speed of sound is dependent ''solely'' upon temperature; see ' below. In such an ideal case, the effects of decreased density and decreased pressure of altitude cancel each other out, save for the residual effect of temperature.
Since temperature (and thus the speed of sound) decreases with increasing altitude up to , sound is refracted
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomen ...

upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source. The decrease of the speed of sound with height is referred to as a negative sound speed gradient.
However, there are variations in this trend above . In particular, in the stratosphere
The stratosphere () is the second layer of the atmosphere of the Earth, located above the troposphere and below the mesosphere. The stratosphere is an atmospheric layer composed of stratified temperature layers, with the warm layers of air ...

above about , the speed of sound increases with height, due to an increase in temperature from heating within the ozone layer
The ozone layer or ozone shield is a region of Earth's stratosphere that absorbs most of the Sun's ultraviolet radiation. It contains a high concentration of ozone (O3) in relation to other parts of the atmosphere, although still small in rela ...

. This produces a positive speed of sound gradient in this region. Still another region of positive gradient occurs at very high altitudes, in the aptly-named thermosphere
The thermosphere is the layer in the Earth's atmosphere directly above the mesosphere and below the exosphere. Within this layer of the atmosphere, ultraviolet radiation causes photoionization/photodissociation of molecules, creating ions; the th ...

above .
Details

Speed of sound in ideal gases and air

For an ideal gas, ''K'' (thebulk modulus
The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume.
Other moduli describe ...

in equations above, equivalent to ''C'', the coefficient of stiffness in solids) is given by
: $K\; =\; \backslash gamma\; \backslash cdot\; p\; .$
Thus, from the Newton–Laplace equation above, the speed of sound in an ideal gas is given by
: $c\; =\; \backslash sqrt,$
where
* ''γ'' is the adiabatic index also known as the ''isentropic expansion factor''. It is the ratio of the specific heat of a gas at constant pressure to that of a gas at constant volume ($C\_p/C\_v$) and arises because a classical sound wave induces an adiabatic compression, in which the heat of the compression does not have enough time to escape the pressure pulse, and thus contributes to the pressure induced by the compression;
* ''p'' is the pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and ...

;
* ''ρ'' is the ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...

law to replace ''p'' with ''nRT''/''V'', and replacing ''ρ'' with ''nM''/''V'', the equation for an ideal gas becomes
: $c\_\; =\; \backslash sqrt\; =\; \backslash sqrt\; =\; \backslash sqrt,$
where
* ''c''Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...

;
* ''γ'' (gamma) is the adiabatic index. At room temperature, where thermal energy is fully partitioned into rotation (rotations are fully excited) but quantum effects prevent excitation of vibrational modes, the value is for diatomic gases (such as oxygen
Oxygen is the chemical element with the chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen Group (periodic table), group in the periodic table, a highly Chemical reaction, reactive nonmetal, and an oxidizing a ...

and nitrogen
Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at seven ...

), according to kinetic theory. Gamma is actually experimentally measured over a range from 1.3991 to 1.403 at , for air. Gamma is exactly for monatomic gases (such as argon
Argon is a chemical element with the symbol Ar and atomic number 18. It is in group 18 of the periodic table and is a noble gas. Argon is the third-most abundant gas in Earth's atmosphere, at 0.934% (9340 ppmv). It is more than twice as ...

) and it is for triatomic molecule gases that, like , are not co-linear (a co-linear triatomic gas such as is equivalent to a diatomic gas for our purposes here);
* ''T'' is the absolute temperature;
* ''M'' is the molar mass of the gas. The mean molar mass for dry air is about ;
* ''n'' is the number of moles;
* ''m'' is the mass of a single molecule.
This equation applies only when the sound wave is a small perturbation on the ambient condition, and the certain other noted conditions are fulfilled, as noted below. Calculated values for ''c''thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of t ...

and so incorrectly used isothermal
In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and ...

calculations instead of adiabatic. His result was missing the factor of ''γ'' but was otherwise correct.
Numerical substitution of the above values gives the ideal gas approximation of sound velocity for gases, which is accurate at relatively low gas pressures and densities (for air, this includes standard Earth sea-level conditions). Also, for diatomic gases the use of requires that the gas exists in a temperature range high enough that rotational heat capacity is fully excited (i.e., molecular rotation is fully used as a heat energy "partition" or reservoir); but at the same time the temperature must be low enough that molecular vibrational modes contribute no heat capacity (i.e., insignificant heat goes into vibration, as all vibrational quantum modes above the minimum-energy-mode have energies that are too high to be populated by a significant number of molecules at this temperature). For air, these conditions are fulfilled at room temperature, and also temperatures considerably below room temperature (see tables below). See the section on gases in specific heat capacity for a more complete discussion of this phenomenon.
For air, we introduce the shorthand
: $R\_*\; =\; R/M\_.$
In addition, we switch to the Celsius
The degree Celsius is the unit of temperature on the Celsius scale (originally known as the centigrade scale outside Sweden), one of two temperature scales used in the International System of Units (SI), the other being the Kelvin scale. The ...

temperature , which is useful to calculate air speed in the region near
0 °C (273 K). Then, for dry air,
$$\backslash begin\; c\_\; \&=\; \backslash sqrt\; =\; \backslash sqrt,\backslash \backslash \; c\_\; \&=\; \backslash sqrt\; \backslash cdot\; \backslash sqrt\; .\; \backslash end$$
Substituting numerical values
$$R\; =\; 8.314\backslash ,462\backslash ,618\backslash ,153\backslash ,24~\backslash mathrm$$
$$M\_\; =\; 0.028\backslash ,964\backslash ,5~\backslash mathrm$$
and using the ideal diatomic gas value of , we have
$$c\_\; \backslash approx\; 331.3\backslash ,\backslash mathrm\; \backslash times\; \backslash sqrt\; .$$
Finally, Taylor expansion of the remaining square root in $\backslash theta$ yields
$$\backslash begin\; c\_\; \&\; \backslash approx\; 331.3\backslash ,\backslash mathrm\; \backslash times\; \backslash left(1\; +\; \backslash frac\backslash right),\backslash \backslash \; \&\; \backslash approx\; 331.3\backslash ,\backslash mathrm\; +\; \backslash theta\; \backslash times\; 0.606\; \backslash ,\backslash mathrm\; .\; \backslash end$$
A graph comparing results of the two equations is to the right, using the slightly more accurate value of for the speed of sound at .
Effects due to wind shear

The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound isrefracted
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomen ...

upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source. Wind shear of 4 m/(s · km) can produce refraction equal to a typical temperature lapse rate of . Higher values of wind gradient will refract sound downward toward the surface in the downwind direction, eliminating the acoustic shadow on the downwind side. This will increase the audibility of sounds downwind. This downwind refraction effect occurs because there is a wind gradient; the sound is not being carried along by the wind.
For sound propagation, the exponential variation of wind speed with height can be defined as follows:
: $U(h)\; =\; U(0)\; h^\backslash zeta,$
: $\backslash frac(h)\; =\; \backslash zeta\; \backslash frac,$
where
* ''U''(''h'') is the speed of the wind at height ''h'';
* ''ζ'' is the exponential coefficient based on ground surface roughness, typically between 0.08 and 0.52;
* ''dU''/''dH''(''h'') is the expected wind gradient at height ''h''.
In the 1862 American Civil War
The American Civil War (April 12, 1861 – May 26, 1865; also known by other names) was a civil war in the United States. It was fought between the Union ("the North") and the Confederacy ("the South"), the latter formed by states ...

Battle of Iuka, an acoustic shadow, believed to have been enhanced by a northeast wind, kept two divisions of Union soldiers out of the battle, because they could not hear the sounds of battle only (six miles) downwind.
Tables

In the standard atmosphere: * ''T''Effect of frequency and gas composition

General physical considerations

The medium in which a sound wave is travelling does not always respond adiabatically, and as a result, the speed of sound can vary with frequency. The limitations of the concept of speed of sound due to extreme attenuation are also of concern. The attenuation which exists at sea level for high frequencies applies to successively lower frequencies as atmospheric pressure decreases, or as themean free path
In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...

increases. For this reason, the concept of speed of sound (except for frequencies approaching zero) progressively loses its range of applicability at high altitudes. The standard equations for the speed of sound apply with reasonable accuracy only to situations in which the wavelength of the sound wave is considerably longer than the mean free path of molecules in a gas.
The molecular composition of the gas contributes both as the mass (M) of the molecules, and their heat capacities, and so both have an influence on speed of sound. In general, at the same molecular mass, monatomic gases have slightly higher speed of sound (over 9% higher) because they have a higher ''γ'' (...) than diatomics do (). Thus, at the same molecular mass, the speed of sound of a monatomic gas goes up by a factor of
: $=\; \backslash sqrt\; =\; \backslash sqrt\; =\; 1.091\backslash ldots$
This gives the 9% difference, and would be a typical ratio for speeds of sound at room temperature in helium
Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table ...

vs. deuterium
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one ...

, each with a molecular weight of 4. Sound travels faster in helium than deuterium because adiabatic compression heats helium more since the helium molecules can store heat energy from compression only in translation, but not rotation. Thus helium molecules (monatomic molecules) travel faster in a sound wave and transmit sound faster. (Sound travels at about 70% of the mean molecular speed in gases; the figure is 75% in monatomic gases and 68% in diatomic gases).
Note that in this example we have assumed that temperature is low enough that heat capacities are not influenced by molecular vibration (see heat capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
Heat capacity ...

). However, vibrational modes simply cause gammas which decrease toward 1, since vibration modes in a polyatomic gas give the gas additional ways to store heat which do not affect temperature, and thus do not affect molecular velocity and sound velocity. Thus, the effect of higher temperatures and vibrational heat capacity acts to increase the difference between the speed of sound in monatomic vs. polyatomic molecules, with the speed remaining greater in monatomics.
Practical application to air

By far, the most important factor influencing the speed of sound in air is temperature. The speed is proportional to the square root of the absolute temperature, giving an increase of about per degree Celsius. For this reason, the pitch of a musical wind instrument increases as its temperature increases. The speed of sound is raised by humidity. The difference between 0% and 100% humidity is about at standard pressure and temperature, but the size of the humidity effect increases dramatically with temperature. The dependence on frequency and pressure are normally insignificant in practical applications. In dry air, the speed of sound increases by about as the frequency rises from to . For audible frequencies above it is relatively constant. Standard values of the speed of sound are quoted in the limit of low frequencies, where the wavelength is large compared to the mean free path. As shown above, the approximate value 1000/3 = 333.33... m/s is exact a little below 5 °C and is a good approximation for all "usual" outside temperatures (in temperate climates, at least), hence the usual rule of thumb to determine how far lightning has struck: count the seconds from the start of the lightning flash to the start of the corresponding roll of thunder and divide by 3: the result is the distance in kilometers to the nearest point of the lightning bolt.Mach number

Mach number, a useful quantity in aerodynamics, is the ratio of airspeed
In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quanti ...

to the local speed of sound. At altitude, for reasons explained, Mach number is a function of temperature.
Aircraft flight instruments, however, operate using pressure differential to compute Mach number, not temperature. The assumption is that a particular pressure represents a particular altitude and, therefore, a standard temperature. Aircraft flight instruments need to operate this way because the stagnation pressure sensed by a Pitot tube
A pitot ( ) tube (pitot probe) measures fluid flow velocity. It was invented by a French engineer, Henri Pitot, in the early 18th century, and was modified to its modern form in the mid-19th century by a French scientist, Henry Darcy. It ...

is dependent on altitude as well as speed.
Experimental methods

A range of different methods exist for the measurement of sound in air. The earliest reasonably accurate estimate of the speed of sound in air was made by William Derham and acknowledged byIsaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the great ...

. Derham had a telescope at the top of the tower of the Church of St Laurence in Upminster
Upminster is a suburban town in East London, England, within the London Borough of Havering. Located east-northeast of Charing Cross, it is one of the district centres identified for development in the London Plan.
Historically a rural villag ...

, England. On a calm day, a synchronized pocket watch would be given to an assistant who would fire a shotgun at a pre-determined time from a conspicuous point some miles away, across the countryside. This could be confirmed by telescope. He then measured the interval between seeing gunsmoke and arrival of the sound using a half-second pendulum. The distance from where the gun was fired was found by triangulation, and simple division (distance/time) provided velocity. Lastly, by making many observations, using a range of different distances, the inaccuracy of the half-second pendulum could be averaged out, giving his final estimate of the speed of sound. Modern stopwatches enable this method to be used today over distances as short as 200–400 metres, and not needing something as loud as a shotgun.
Single-shot timing methods

The simplest concept is the measurement made using twomicrophone
A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and pu ...

s and a fast recording device such as a digital storage scope. This method uses the following idea.
If a sound source and two microphones are arranged in a straight line, with the sound source at one end, then the following can be measured:
# The distance between the microphones (''x''), called microphone basis.
# The time of arrival between the signals (delay) reaching the different microphones (''t'').
Then ''v'' = ''x''/''t''.
Other methods

In these methods, thetime
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...

measurement has been replaced by a measurement of the inverse of time (frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

).
Kundt's tube is an example of an experiment which can be used to measure the speed of sound in a small volume. It has the advantage of being able to measure the speed of sound in any gas. This method uses a powder to make the nodes and antinode
A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effec ...

s visible to the human eye. This is an example of a compact experimental setup.
A tuning fork
A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against ...

can be held near the mouth of a long pipe which is dipping into a barrel of water
Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...

. In this system it is the case that the pipe can be brought to resonance if the length of the air column in the pipe is equal to ''(1 + 2''n'')λ/4'' where ''n'' is an integer. As the antinodal point for the pipe at the open end is slightly outside the mouth of the pipe it is best to find two or more points of resonance and then measure half a wavelength between these.
Here it is the case that ''v'' = ''fλ''.
High-precision measurements in air

The effect of impurities can be significant when making high-precision measurements. Chemical desiccants can be used to dry the air, but will, in turn, contaminate the sample. The air can be dried cryogenically, but this has the effect of removing the carbon dioxide as well; therefore many high-precision measurements are performed with air free of carbon dioxide rather than with natural air. A 2002 review found that a 1963 measurement by Smith and Harlow using a cylindrical resonator gave "the most probable value of the standard speed of sound to date." The experiment was done with air from which the carbon dioxide had been removed, but the result was then corrected for this effect so as to be applicable to real air. The experiments were done at but corrected for temperature in order to report them at . The result was for dry air at STP, for frequencies from to .Non-gaseous media

Speed of sound in solids

Three-dimensional solids

In a solid, there is a non-zero stiffness both for volumetric deformations and shear deformations. Hence, it is possible to generate sound waves with different velocities dependent on the deformation mode. Sound waves generating volumetric deformations (compression) and shear deformations (shearing) are called pressure waves (longitudinal waves) and shear waves (transverse waves), respectively. Inearthquake
An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, from ...

s, the corresponding seismic waves are called P-wave
A P wave (primary wave or pressure wave) is one of the two main types of elastic body waves, called seismic waves in seismology. P waves travel faster than other seismic waves and hence are the first signal from an earthquake to arrive at any ...

s (primary waves) and S-waves (secondary waves), respectively. The sound velocities of these two types of waves propagating in a homogeneous 3-dimensional solid are respectively given byL. E. Kinsler et al. (2000), ''Fundamentals of acoustics'', 4th Ed., John Wiley and sons Inc., New York, USA.
: $c\_\; =\; \backslash sqrt\; =\; \backslash sqrt,$
: $c\_\; =\; \backslash sqrt,$
where
* ''K'' is the bulk modulus
The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume.
Other moduli describe ...

of the elastic materials;
* ''G'' is the Young's modulus
Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied le ...

;
* ''ρ'' is the density;
* ''ν'' is Poisson's ratio.
The last quantity is not an independent one, as . Note that the speed of pressure waves depends both on the pressure and shear resistance properties of the material, while the speed of shear waves depends on the shear properties only.
Typically, pressure waves travel faster in materials than do shear waves, and in earthquakes this is the reason that the onset of an earthquake is often preceded by a quick upward-downward shock, before arrival of waves that produce a side-to-side motion. For example, for a typical steel alloy, , and , yielding a compressional speed ''c''One-dimensional solids

The speed of sound for pressure waves in stiff materials such as metals is sometimes given for "long rods" of the material in question, in which the speed is easier to measure. In rods where their diameter is shorter than a wavelength, the speed of pure pressure waves may be simplified and is given by: : $c\_\; =\; \backslash sqrt,$ where ''E'' isYoung's modulus
Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied le ...

. This is similar to the expression for shear waves, save that Young's modulus
Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied le ...

replaces the Speed of sound in liquids

In a fluid, the only non-zerostiffness
Stiffness is the extent to which an object resists deformation in response to an applied force.
The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.
Calculations
The stiffness, k, of a bo ...

is to volumetric deformation (a fluid does not sustain shear forces).
Hence the speed of sound in a fluid is given by
: $c\_\; =\; \backslash sqrt,$
where ''K'' is the Water

In fresh water, sound travels at about at (see the External Links section below for online calculators). Applications ofunderwater sound
Underwater acoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water, its contents and its boundaries. The water may be in the ocean, a lake, a river or a tank. Typ ...

can be found in sonar
Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, measure distances ( ranging), communicate with or detect objects on ...

, acoustic communication and acoustical oceanography.
Seawater

In salt water that is free of air bubbles or suspended sediment, sound travels at about ( at , 10°C and 3%salinity
Salinity () is the saltiness or amount of salt dissolved in a body of water, called saline water (see also soil salinity). It is usually measured in g/L or g/kg (grams of salt per liter/kilogram of water; the latter is dimensionless and equal ...

by one method). The speed of sound in seawater depends on pressure (hence depth), temperature (a change of ~ ), and salinity
Salinity () is the saltiness or amount of salt dissolved in a body of water, called saline water (see also soil salinity). It is usually measured in g/L or g/kg (grams of salt per liter/kilogram of water; the latter is dimensionless and equal ...

(a change of 1‰
Per mille (from Latin , "in each thousand") is an expression that means parts per thousand. Other recognised spellings include per mil, per mill, permil, permill, or permille.
The associated sign is written , which looks like a percent sig ...

~ ), and empirical equations have been derived to accurately calculate the speed of sound from these variables. 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). For more information see Dushaw et al.
An empirical equation for the speed of sound in sea water is provided by Mackenzie:
: $c(T,\; S,\; z)\; =\; a\_1\; +\; a\_2\; T\; +\; a\_3\; T^2\; +\; a\_4\; T^3\; +\; a\_5\; (S\; -\; 35)\; +\; a\_6\; z\; +\; a\_7\; z^2\; +\; a\_8\; T(S\; -\; 35)\; +\; a\_9\; T\; z^3,$
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''for an online calculator. (Note: 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 and the Chen-Millero-Li Equation.

Speed of sound in plasma

The speed of sound in a Plasma (physics), plasma for the common case that the electrons are hotter than the ions (but not too much hotter) is given by the formula (see here) : $c\_s\; =\; (\backslash gamma\; ZkT\_\backslash mathrm/m\_\backslash mathrm)^\; =\; 90.85\; (\backslash gamma\; ZT\_e/\backslash mu)^~\backslash mathrm,$ where * ''m''ion
An ion () is an atom or molecule with a net electrical charge.
The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by convent ...

mass;
* ''μ'' is the ratio of ion mass to proton
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...

mass ;
* ''T''electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kno ...

temperature;
* ''Z'' is the charge state;
* ''k'' is Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...

;
* ''γ'' is the adiabatic index.
In contrast to a gas, the pressure and the density are provided by separate species: the pressure by the electrons and the density by the ions. The two are coupled through a fluctuating electric field.
Mars

The speed of sound onMars
Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin atmo ...

varies as a function of frequency. Higher frequencies travel faster than lower frequencies. Higher frequency sound from lasers travels at , while low frequency sound topped out at .
Gradients

When sound spreads out evenly in all directions in three dimensions, the intensity drops in proportion to the inverse square of the distance. However, in the ocean, there is a layer called the 'deep sound channel' or SOFAR channel which can confine sound waves at a particular depth. In the SOFAR channel, the speed of sound is lower than that in the layers above and below. Just as light waves will refract towards a region of higherrefractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...

, sound waves will refract
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomen ...

towards a region where their speed is reduced. The result is that sound gets confined in the layer, much the way light can be confined to a sheet of glass or optical fiber
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means ...

. Thus, the sound is confined in essentially two dimensions. In two dimensions the intensity drops in proportion to only the inverse of the distance. This allows waves to travel much further before being undetectably faint.
A similar effect occurs in the atmosphere. Project Mogul successfully used this effect to detect a nuclear explosion
A nuclear explosion is an explosion that occurs as a result of the rapid release of energy from a high-speed nuclear reaction. The driving reaction may be nuclear fission or nuclear fusion or a multi-stage cascading combination of the two, tho ...

at a considerable distance.
See also

* Acoustoelastic effect * Elastic wave * Second sound *Sonic boom
A sonic boom is a sound associated with shock waves created when an object travels through the air faster than the speed of sound. Sonic booms generate enormous amounts of sound energy, sounding similar to an explosion or a thunderclap to ...

* Sound barrier
* Speeds of sound of the elements
* Underwater acoustics
Underwater acoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water, its contents and its boundaries. The water may be in the ocean, a lake, a river or a tank. Typ ...

* Vibrations
References

External links

Speed of Sound Calculator

Speed of sound: Temperature Matters, Not Air Pressure

How to Measure the Speed of Sound in a Laboratory

* ttp://www.dosits.org/ Discovery of Sound in the Sea(uses of sound by humans and other animals) {{Authority control Fluid dynamics Aerodynamics Acoustics Sound Sound measurements Physical quantities Chemical properties Velocity Temporal rates