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| {{other uses}}
| | A superb tip to consider if you want to be sure you never obtain a candida albicans would be to always wear clothing that is manufactured from natural resources. If you have a candida yeast infection, you will see one or all three of the following:. Simple apply it to your area and it will soothe the symptoms. Strong immunity systems easily fight off yeast infections. Over-the-counter treatments are usually antifungal drugs in the form of creams, ointments, sprays, powders, tablets, etc. <br><br>No matter how long you have searched for a solution I want to reassure you a holistic approach will end your search. Treating yeast infection with hydrogen peroxide is one of the best methods you could ever use for treating yeast infections. To fight yeast infection, use unscented products and avoid scented feminine hygiene products because they irritate the vagina and promote itching. Treating your symptoms and not addressing the root of the infection is what a lot of the over the counter yeast infection treatments will give you. Vaginal discharge that looks like cottage cheese. <br><br>To take care of the signs, a clove can be peeled and inserted in the vagina in the form of a suppository. They are much larger - about 10 times more than the bacterial cells, moreover yeast cells may be found to be oval in shape unlike the bacterial cells which are mostly elongated. When the skin is already infected by bacteria and fungus, it can easily spread all over and most of time with swelling. Penicillin was the first fungus to go to medical school but not the last. There are in fact, alternative, cheap, safe, natural and holistic health practices and methods necessary to permanently eliminate the symptoms of this disease and cure the root internal cause of yeast infection regardless of its type, location, or level of severity. <br><br>When what are known as candida albicans, the bad yeast, overgrow in your body you develop a yeast infection. Male yeast infection can be healed almost as the same as vaginal yeast infection is treated. Wearing the wrong type of clothing can actually help your body foster a Yeast Infections. Use natural way to cure yeast infection in women within 12 hours. The Candida fungus which is responsible for the occurrence of the infection is naturally present in our body making us prone to the infection. <br><br>They are loaded with fiber, protein, omega 3 and antioxidants. The Candida yeast lives naturally in everyone's vagina, and using anti fungal cream when it's not needed will cause the yeast to mutate into an aggressive fungus, and then it will become resistant. Usually, steroids and antibiotics are two common reasons that females seek a remedy for yeast infection. The yeast infection symptom a person gets depends on where the infection is located and on how severe the infection is. Of course, you can use probiotics capsules and suppositories from the pharmacy as an alternative.<br><br>If you have any inquiries pertaining to where and how to use over the counter yeast infection medication; [http://www.naturalcureyeastinfection.info/sitemap/ http://www.naturalcureyeastinfection.info/sitemap/],, you could contact us at our web-site. |
| {{Sound measurements}}
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| The '''speed of sound''' is the distance travelled during a unit of time by a [[sound wave]] propagating through an [[elasticity (solid mechanics)|elastic]] medium. In dry [[air]] at {{Convert|20|°C}}, the speed of sound is {{Convert|343.2|m/s|ft/s|0|sp=en}}. This is {{Convert|1234|km/h|mph|0|sp=en}}, or about a kilometre in three seconds or a mile in five seconds.
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| In [[fluid dynamics]], the speed of sound in a fluid medium (gas or liquid) is used as a relative measure of speed itself. The speed of an object divided by the speed of sound in the fluid is called the [[Mach number]]. Objects moving at speeds greater than ''{{gaps|Mach|1}}'' are traveling at [[supersonic]] speeds.
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| The speed of sound in an [[ideal gas]] is independent of frequency, but does vary slightly with frequency in a real gas. It is proportional to the square root of the [[absolute temperature]], but is independent of [[pressure]] or [[density]] for a given ideal gas. Sound speed in air varies slightly with pressure only because air is not quite an ideal gas. In addition, for different gases, the speed of sound is inversely proportional to the mean [[molecular weight]] of the gas, and is affected to a lesser extent by the number of ways in which the [[molecules]] of the gas can store [[heat]] from [[compression (physical)|compression]], since sound in gases is a compression wave. Although (in the case of gases only) the speed of sound is expressed in terms of a ratio of ''both'' density and pressure, these quantities cancel in ideal gases at any given temperature, composition, and heat capacity. This leads to a velocity formula for ideal gases which includes only the latter independent variables.
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| In common everyday speech, ''speed of sound'' refers to the speed of sound waves in [[Earth's atmosphere|air]]. However, the speed of sound varies from substance to substance. Sound travels faster in [[liquids]] and non-porous [[solids]] than it does in air. It travels about 4.3 times as fast in [[water]] (1,484 m/s), and nearly 15 times as fast in iron (5,120 m/s), than in air at 20 degrees Celsius. Sound waves in solids are composed of compression waves (just as in gases and liquids), but there is also a different type of sound wave called a [[shear wave]], which occurs only in solids. These different types of waves in solids usually travel at different speeds, as exhibited in [[seismology]]. The speed of a compression sound wave in solids is determined by the medium's [[compressibility]], [[shear modulus]] and density. The speed of shear waves is determined only by the solid material's shear modulus and density.
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| ==Basic concept==
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| The transmission of sound can be illustrated by using a [[toy model]] consisting of an array of balls interconnected by springs. For real material
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| the balls represent molecules and the springs represent the bonds between them. Sound passes through the model by compressing and expanding the springs, transmitting energy to neighboring balls, which transmit energy to ''their'' springs, and so on. The speed of sound through the model depends on the stiffness of the springs (stiffer springs transmit energy more quickly). Effects like dispersion and reflection can also be understood using this model.
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| In a real material, the stiffness of the springs is called the [[elastic modulus]], and the mass corresponds to the [[density]]. All other things being equal ([[ceteris paribus]]), sound will travel more slowly in spongy materials, and faster in stiffer ones. 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 ([[Hydrogen-1|protium]]) gas than in heavy hydrogen ([[deuterium]]) 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.
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| Some textbooks mistakenly state that the speed of sound increases with increasing density. This is usually illustrated by presenting data for three materials, such as air, water and steel, which also have vastly different compressibilities which more than make 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.
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| ===Compression and shear waves===
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| [[File:Onde compression impulsion 1d 30 petit.gif|thumb|305px|Pressure-pulse or compression-type wave ([[longitudinal wave]]) confined to a plane. This is the only type of sound wave that travels in fluids (gases and liquids)]]
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| [[File:Onde cisaillement impulsion 1d 30 petit.gif|thumb|305px|[[Transverse wave]] affecting atoms initially confined to a plane. This additional type of sound wave (additional type of elastic wave) travels only in solids, and the sideways shearing motion may take place in '''any''' direction at right angles to the direction of wave-travel (only one shear direction is shown here, at right angles to the plane). Furthermore, the right-angle shear direction may change over time and distance, resulting in different types of polarization of shear-waves]]
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| In a gas or liquid, sound consists of compression waves. In solids, waves propagate as two different types. A [[longitudinal wave]] is associated with compression and decompression in the direction of travel, which is the same process as all sound waves in gases and liquids. A [[transverse wave]], called a [[shear wave]] in solids, is due to elastic deformation of the medium perpendicular to the direction of wave travel; the direction of shear-deformation is called the "[[Polarization (waves)|polarization]]" of this type of wave. In general, transverse waves occur as a pair of [[orthogonal]] 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]], where sharp compression waves arrive first, and rocking transverse waves seconds later.
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| The speed of a compression wave in fluid is determined by the medium's [[compressibility]] and [[density]]. In solids, the compression waves are analogous to those in fluids, depending on compressibility, density, and the additional factor of [[shear modulus]]. The speed of shear waves, which can occur only in solids, is determined simply by the solid material's shear modulus and density.
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| ==Equations==
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| In general, the speed of sound ''c'' is given by the Newton-Laplace equation:
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| :<math>
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| c = \sqrt{\frac{K}{\rho}}\,
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| </math>
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| where
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| :''K'' is a coefficient of stiffness, the [[bulk modulus]] (or the modulus of bulk elasticity for gases),
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| :<math>\rho</math> is the [[density]]
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| 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 the density. For ideal gases the bulk modulus '''P''' is simply the gas pressure multiplied by the [[adiabatic index]].
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| For general [[equations of state]], if [[classical mechanics]] is used, the speed of sound <math>c</math> is given by
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| :<math>
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| c^2=\left(\frac{\partial p}{\partial\rho}\right)_s</math>
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| where <math>p</math> is the pressure and <math>\rho</math> is the density and the [[derivative]] is taken adiabatically, that is, at constant [[entropy]] per particle (''s'').
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| If [[special relativity|relativistic]] effects are important, the speed of sound is calculated from the [[relativistic Euler equations]].
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| In a '''non-dispersive medium''' sound speed is independent of [[sound frequency]], so the speeds of energy transport and sound propagation are the same for all sound frequencies. For audible sounds, the mixture of oxygen and nitrogen constitutes a non-dispersive medium. However, air does contain a small amount of CO<sub>2</sub> which ''is'' a dispersive medium, and it introduces dispersion to air at [[ultrasound|ultrasonic]] frequencies (> 28 [[kHz]]).<ref>Dean, E. A. (August 1979). [http://handle.dtic.mil/100.2/ADA076060 Atmospheric Effects on the Speed of Sound], Technical report of Defense Technical Information Center</ref>
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| In a '''dispersive medium''' sound speed is a function of sound frequency, through the [[dispersion relation]]. The spatial and temporal distribution of a propagating disturbance will continually change. Each frequency component propagates at its own [[phase velocity]], while the energy of the disturbance propagates at the [[group velocity]]. The same phenomenon occurs with light waves; see [[Dispersion (optics)#Group and phase velocity|optical dispersion]] for a description.
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| ==Dependence on the properties of the medium==
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| 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 depend on the shear deformation under shear stress (called the [[shear modulus]]), 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]].
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| In fluids, only the medium's compressibility and density are the important factors, since fluids do not tolerate 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]].
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| In gases, adiabatic compressibility is directly related to pressure through the [[heat capacity ratio]] (adiabatic index), and pressure and density are inversely related at a given temperature and composition, thus making only the latter independent properties (temperature, molecular composition, and heat capacity ratio) important. In low [[molecular weight]] gases, such as [[helium]], sound propagates faster compared to heavier gases, such as [[xenon]] (for monatomic gases the speed of sound is about 75% of the mean speed that molecules move in the gas). For a given [[ideal gas]] the sound speed depends only on its [[temperature]]. At a constant temperature, the ideal gas [[pressure]] has no effect on the speed of sound, because pressure and [[density]] (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 (see derivations below). Thus, for a single given gas (where molecular weight does not change) and over a small temperature range (where heat capacity is relatively constant), the speed of sound becomes dependent on only the temperature of the gas.
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| In non-ideal gases, such as a [[Van der Waals equation|van der Waals gas]], the proportionality is not exact, and there is a slight dependence of sound velocity on the gas pressure.
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| Humidity has a small but measurable effect on sound speed (causing it to increase by about 0.1%-0.6%), because [[oxygen]] and [[nitrogen]] molecules of the air are replaced by lighter molecules of [[water]]. This is a simple mixing effect.
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| ==Altitude variation and implications for atmospheric acoustics==
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| [[File:Comparison US standard atmosphere 1962.svg|thumb|250px|Density and pressure decrease smoothly with altitude, but temperature (red) does not. The speed of sound (blue) depends only on the complicated temperature variation at altitude and can be calculated from it, since isolated density and pressure effects on sound speed cancel each other. Speed of sound increases with height in two regions of the stratosphere and thermosphere, due to heating effects in these regions.]]
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| In the [[Earth's atmosphere]], the chief factor affecting the speed of sound is the [[temperature]]. For a given ideal gas with constant heat capacity and composition, sound speed is dependent ''solely'' upon temperature; see [[Speed of sound#Details|Details]] 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.
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| Since temperature (and thus the speed of sound) decreases with increasing altitude up to 11 km, sound is [[refraction|refracted]] upward, away from listeners on the ground, creating an [[acoustic shadow]] at some distance from the source.<ref name="Everest2001">
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| {{cite book
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| | last = Everest
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| | first = F.
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| | title = The Master Handbook of Acoustics
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| | publisher = McGraw-Hill
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| | location = New York
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| | year = 2001
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| | isbn = 0-07-136097-2
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| | pages = 262–263 }}
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| </ref> The decrease of the sound speed with height is referred to as a negative [[sound speed gradient]].
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| However, there are variations in this trend above 11 km. In particular, in the [[stratosphere]] above about 20 km, the speed of sound increases with height, due to an increase in temperature from heating within the [[ozone layer]]. This produces a positive sound speed gradient in this region. Still another region of positive gradient occurs at very high altitudes, in the aptly-named [[thermosphere]] above 90 km.
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| ==Practical formula for dry air==
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| [[File:Speed of sound in dry air.svg|thumb|350px|Approximation of the speed of sound in dry air based on the [[heat capacity ratio]] (in green) against the truncated [[Taylor expansion]] (in red).]]
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| The approximate speed of sound in dry (0% humidity) air, in meters per second ('''m·s<sup>−1</sup>'''), at temperatures near 0 °C, can be calculated from:
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| :<math>
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| c_{\mathrm{air}} = (331{.}3 + 0{.}606 \cdot \vartheta) \ \mathrm{m \cdot s^{-1}}\,
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| </math>
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| where <math>\vartheta</math> is the temperature in degrees [[Celsius]] (°C).
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| This equation is derived from the first two terms of the [[Taylor expansion]] of the following more accurate equation:
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| :<math>c_{\mathrm{air}} = 331.3\,\mathrm{m \cdot s^{-1}} \sqrt{1+\frac{\vartheta}{273.15}}</math>
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| Dividing the first part, and multiplying the second part, on the right hand side, by <math>\sqrt{273.15}</math> gives the exactly equivalent form:
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| :<math>c_{\mathrm{air}} = 20.0457\,\mathrm{m \cdot s^{-1}} \sqrt{{\vartheta}+ {273.15\;}}</math>
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| The value of 331.3 m/s, which represents the speed at 0 °C (or 273.15 K), is based on theoretical (and some measured) values of the [[heat capacity ratio]], <math>\gamma</math>, as well as on the fact that at 1 [[atmosphere (unit)|atm]] real air is very well described by the ideal gas approximation. Commonly found values for the speed of sound at 0 °C may vary from 331.2 to 331.6 due to the assumptions made when it is calculated. If ideal gas <math>\gamma</math> is assumed to be 7/5 = 1.4 exactly, the 0 °C speed is calculated (see section below) to be 331.3 m/s, the coefficient used above.
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| This equation is correct to a much wider temperature range, but still depends on the approximation of heat capacity ratio being independent of temperature, and for this reason will fail, particularly at higher temperatures. It gives good predictions in relatively dry, cold, low pressure conditions, such as the Earth's [[stratosphere]]. The equation fails at extremely low pressures and short wavelengths, due to dependence on the assumption that the wavelength of the sound in the gas is much longer than the average [[mean free path]] between gas molecule collisions. A derivation of these equations will be given in the following section.
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| A graph comparing results of the two equations is at right, using the slightly different value of 331.5 m/s for the speed of sound at 0°C.
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| ==Details==
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| ===Speed in ideal gases and in air===<!-- This section is linked from [[Supersonic]] -->
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| For a gas, ''K'' (the [[bulk modulus]] in equations above, equivalent to C, the coefficient of stiffness in solids) is approximately given by
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| :<math>
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| K = \gamma \cdot p\,
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| </math>
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| thus
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| :<math>
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| c = \sqrt{\gamma \cdot {p \over \rho}}\,
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| </math>
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| Where:
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| :<math>\gamma</math> is the [[adiabatic index]] also known as the ''isentropic expansion factor''. It is the ratio of specific heats of a gas at a constant-pressure to a gas at a constant-volume(<math>C_p/C_v</math>), 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.
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| :''p'' is the [[pressure]].
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| :''<math>\rho</math>'' is the [[density]]
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| Using the [[ideal gas]] law to replace <math>p</math> with ''nRT''/''V'', and replacing ''ρ'' with ''nM''/''V'', the equation for an ideal gas becomes:
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| :<math>
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| c_{\mathrm{ideal}} = \sqrt{\gamma \cdot {p \over \rho}} = \sqrt{\gamma \cdot R \cdot T \over M}= \sqrt{\gamma \cdot k \cdot T \over m}\,
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| </math>
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| where
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| *<math>c_{\mathrm{ideal}} </math> is the speed of sound in an [[ideal gas]].
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| *<math>R</math> (approximately 8.3145 J·mol<sup>−1</sup>·K<sup>−1</sup>) is the [[molar gas constant]].<ref>{{cite web|url=http://physics.nist.gov/cgi-bin/cuu/Value?r |title=CODATA Value: molar gas constant |publisher=Physics.nist.gov |date= |accessdate=2010-10-24}}</ref>
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| *<math>k</math> is the [[Boltzmann constant]]
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| *<math>\gamma</math> (gamma) is the [[adiabatic index]] (sometimes assumed 7/5 = 1.400 for diatomic molecules from kinetic theory, assuming from quantum theory a temperature range at which thermal energy is fully partitioned into rotation (rotations are fully excited), but none into vibrational modes. Gamma is actually experimentally measured over a range from 1.3991 to 1.403 at 0 degrees Celsius, for air. Gamma is assumed from kinetic theory to be exactly 5/3 = 1.6667 for monatomic molecules such as [[noble gas]]es).
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| *<math>T</math> is the absolute temperature in [[kelvin]].
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| *<math>M</math> is the molar mass in [[kilogram]]s per [[mole (unit)|mole]]. The mean molar mass for dry air is about 0.0289645 kg/mol.
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| *<math>m</math> is the mass of a single molecule in kilograms.
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| 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 <math>c_{\mathrm{air}}</math> have been found to vary slightly from experimentally determined values.<ref name=USSA1976>U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976.</ref>
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| [[Isaac Newton|Newton]] famously considered the speed of sound before most of the development of [[thermodynamics]] and so incorrectly used [[isothermal]] calculations instead of [[adiabatic]]. His result was missing the factor of <math>\gamma</math> but was otherwise correct.
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| 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 <math>\ \gamma\, = 1.4000 </math> requires that the gas exist 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 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.
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| For air, we use a simplified symbol <math>\ R_* = R/M_{\mathrm{air}}</math>.
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| Additionally, if temperatures in degrees [[Celsius]](°C) are to be used to calculate air speed in the region near 273 kelvin, then Celsius temperature <math>\vartheta = T - 273.15 </math> may be used. Then:
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| :<math>
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| c_{\mathrm{ideal}} = \sqrt{\gamma \cdot R_* \cdot T} = \sqrt{\gamma \cdot R_* \cdot (\vartheta + 273.15)}\,
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| </math>
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| :<math>
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| c_{\mathrm{ideal}} = \sqrt{\gamma \cdot R_* \cdot 273.15} \cdot \sqrt{1+\frac{\vartheta}{273.15}}\,
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| </math>
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| For dry air, where <math>\vartheta\, </math> (theta) is the temperature in degrees [[Celsius]](°C).
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| Making the following numerical substitutions:
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| :<math>
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| \ R = 8.314510 \cdot \mathrm{J \cdot mol^{-1}} \cdot K^{-1}\,
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| </math>
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| is the molar [[gas constant]] in J/mole/Kelvin;
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| :<math>
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| \ M_{\mathrm{air}} = 0.0289645 \cdot \mathrm{kg \cdot mol^{-1}}\,
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| </math>
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| is the mean molar mass of air, in kg; and using the ideal diatomic gas value of <math>\ \gamma\, = 1.4000\,</math>
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| Then:
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| :<math>
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| c_{\mathrm{air}} = 331.3 \ \mathrm{\frac{m}{s}} \sqrt{1+\frac{\vartheta^{\circ}\mathrm{C}}{273.15\;^{\circ}\mathrm{C}}}\,
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| </math>
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| Using the first two terms of the Taylor expansion:
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| :<math>
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| c_{\mathrm{air}} = 331.3 \ \mathrm{\frac{m}{s}} (1 + \frac{\vartheta^{\circ}\mathrm{C}}{2 \cdot 273.15\;^{\circ}\mathrm{C}})\,
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| </math>
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| :<math>
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| c_{\mathrm{air}} = ( 331{.}3 + 0{.}606\;^{\circ}\mathrm{C}^{-1} \cdot \vartheta)\ \mathrm{ \frac{m}{s}}\,</math>
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| The derivation includes the first two equations given in the ''Practical formula for dry'' air section above.
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| ===Effects due to wind shear===
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| The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound is [[refraction|refracted]] upward, away from listeners on the ground, creating an [[acoustic shadow]] at some distance from the source.<ref name="Everest2001" /> Wind shear of 4 m·s<sup>−1</sup>·km<sup>−1</sup> can produce refraction equal to a typical temperature [[lapse rate]] of 7.5 °C/km.<ref>{{cite book | last = Uman | first = Martin | title = Lightning | publisher = Dover Publications | location = New York | year = 1984 | isbn = 0-486-64575-4 }}</ref> Higher values of wind gradient will refract sound downward toward the surface in the downwind direction,<ref>{{cite book | last = Volland | first = Hans | title = Handbook of Atmospheric Electrodynamics | publisher = CRC Press | location = Boca Raton | year = 1995 | isbn = 0-8493-8647-0 | page = 22}}</ref> 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.<ref>{{cite book | last = Singal | first = S. | title = Noise Pollution and Control Strategy | publisher = Alpha Science International, Ltd | location = | year = 2005 | isbn = 1-84265-237-0 | page = 7 | quote = It may be seen that refraction effects occur only because there is a wind gradient and it is not due to the result of sound being convected along by the wind.}}</ref>
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| For sound propagation, the exponential variation of wind speed with height can be defined as follows:<ref name=Bies>{{cite book | last = Bies | first = David | title = Engineering Noise Control; Theory and Practice | publisher = Spon Press | location = London | year = 2004 | isbn = 0-415-26713-7 | page = 235 | quote = As wind speed generally increases with altitude, wind blowing towards the listener from the source will refract sound waves downwards, resulting in increased noise levels.}}</ref>
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| :<math>
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| \ U(h) = U(0) h ^ \zeta\,
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| </math>
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| :<math>
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| \ \frac {dU} {dH} = \zeta \frac {U(h)} {h}\,
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| </math>
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| where:
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| :<math>\ U(h)</math> = speed of the wind at height <math> \ h</math>, and <math> \ U(0)</math> is a constant
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| :<math>\ \zeta</math> = exponential coefficient based on ground surface roughness, typically between 0.08 and 0.52
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| :<math>\ \frac {dU} {dH}</math> = expected wind gradient at height <math> h</math>
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| In the 1862 [[American Civil War]] [[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,<ref>{{cite book | last = Cornwall | first = Sir | title = Grant as Military Commander | publisher = Barnes & Noble Inc | location = | year = 1996 | isbn = 1-56619-913-1 pages = p. 92}}</ref> because they could not hear the sounds of battle only 10 km (six miles) downwind.<ref>{{cite book | last = Cozzens | first = Peter | title = The Darkest Days of the War: the Battles of Iuka and Corinth | publisher = The University of North Carolina Press | location = Chapel Hill | year = 2006 | isbn = 0-8078-5783-1 }}</ref>
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| ===Tables===
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| In the [[Standard temperature and pressure|standard atmosphere]]:
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| *''T''<sub>0</sub> is 273.15 K (= 0 °C = 32 °F), giving a theoretical value of 331.3 m·s<sup>−1</sup> (= 1086.9 ft/s = 1193 km·h<sup>−1</sup> = 741.1 mph = 644.0 [[Knot (unit)|knots]]). Values ranging from 331.3-331.6 may be found in reference literature, however.
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| *''T''<sub>20</sub> is 293.15 K (= 20 °C = 68 °F), giving a value of 343.2 m·s<sup>−1</sup> (= 1126.0 ft/s = 1236 km·h<sup>−1</sup> = 767.8 mph = 667.2 [[Knot (unit)|knots]]).
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| *''T''<sub>25</sub> is 298.15 K (= 25 °C = 77 °F), giving a value of 346.1 m·s<sup>−1</sup> (= 1135.6 ft/s = 1246 km·h<sup>−1</sup> = 774.3 mph = 672.8 [[Knot (unit)|knots]]).
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| | |
| In fact, assuming an [[ideal gas]], the speed of sound ''c'' depends on temperature 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''.
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| | |
| {{Temperature_effect}}
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| | |
| Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:
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| | |
| {| class="wikitable"
| |
| |- style="background:#f0f0f0;"
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| |'''Altitude'''
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| |'''Temperature'''
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| |'''m·s<sup>−1</sup>'''
| |
| |'''km·h<sup>−1</sup>'''
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| |'''mph'''
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| |'''knots'''
| |
| |-
| |
| |Sea level
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| |15 °C (59 °F)
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| |340
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| |1225
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| |761
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| |661
| |
| |-
| |
| |11,000 m−20,000 m<br>(Cruising altitude of commercial jets,<br>and [[Bell X-1|first supersonic flight]])
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| | −57 °C (−70 °F)
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| |295
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| |1062
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| |660
| |
| |573
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| |-
| |
| |29,000 m (Flight of [[Boeing X-43|X-43A]])
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| | −48 °C (−53 °F)
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| |301
| |
| |1083
| |
| |673
| |
| |585
| |
| |}
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| | |
| ==Effect of frequency and gas composition==
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| 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.<ref>[[Albert Beaumont Wood|A B Wood]], A Textbook of Sound (Bell, London, 1946)</ref>
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| | |
| 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 the [[mean free path]] increases. For this reason, the concept of speed of sound (except for frequencies approaching zero) progressively loses its range of applicability at high altitudes.<ref name="USSA1976"/> The standard equations for the speed of sound apply with reasonable accuracy only to situations in which the wavelength of the soundwave is considerably longer than the mean free path of molecules in a gas.
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| | |
| 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 sound speeds (over 9% higher) because they have a higher <math>\gamma</math> (5/3 = 1.66...) than diatomics do (7/5 = 1.4). Thus, at the same molecular mass, the sound speed of a monatomic gas goes up by a factor of
| |
| | |
| <math>{ c_{\mathrm{gas: monatomic}} \over c_{\mathrm{gas: diatomic}} } = \sqrt{{{{5 / 3} \over {7 / 5}}}} = \sqrt{25 \over 21} </math> = 1.091...
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| | |
| This gives the 9% difference, and would be a typical ratio for sound speeds at room temperature in [[helium]] vs. [[deuterium]], 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 generally travels at about 70% of the mean molecular speed in gases).
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| | |
| 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]]). However, vibrational modes simply cause gammas which decrease toward 1, since vibration modes in a polyatomic gas gives 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 sound speed in monatomic vs. polyatomic molecules, with the speed remaining greater in monatomics.
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| ==Mach number==
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| {{main|Mach number}}
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| [[File:FA-18 Hornet breaking sound barrier (7 July 1999) - filtered.jpg|right|thumb|U.S. Navy [[F/A-18 Hornet|F/A-18]] traveling near the speed of sound. The white halo consists of condensed water droplets formed by the sudden drop in air pressure behind the shock cone around the aircraft (see [[Prandtl-Glauert singularity]]).<ref>{{cite web|url=http://antwrp.gsfc.nasa.gov/apod/ap070819.html |title=APOD: 19 August 2007- A Sonic Boom |publisher=Antwrp.gsfc.nasa.gov |date= |accessdate=2010-10-24}}</ref>]]
| |
| Mach number, a useful quantity in aerodynamics, is the ratio of air [[speed]] 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]] is dependent on altitude as well as speed.
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| ==Experimental methods==
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| A range of different methods exist for the measurement of sound in air.
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| | |
| The earliest reasonably accurate estimate of the speed of sound in air was made by [[William Derham]], and acknowledged by [[Isaac Newton]]. Derham had a telescope at the top of the tower of the [[Church of St Laurence, Upminster|Church of St Laurence]] in [[Upminster]], 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 noise using a half-second pendulum. The distance from where the gun was fired was found by triangulation, and simple division (time / distance) 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 meters, and not needing something as loud as a shotgun.
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| | |
| ===Single-shot timing methods===
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| The simplest concept is the measurement made using two [[microphone]]s and a fast recording device such as a [[Digital data|digital]] storage scope. This method uses the following idea.
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| | |
| 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:
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| | |
| 1. The distance between the microphones (''x''), called microphone basis.
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| 2. The time of arrival between the signals (delay) reaching the different microphones (''t'')
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| | |
| Then ''v'' = ''x'' / ''t''
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| ===Other methods===
| |
| In these methods the [[time]] measurement has been replaced by a measurement of the inverse of time ([[frequency]]).
| |
| | |
| [[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 [[Node (physics)|nodes]] and [[antinode]]s visible to the human eye. This is an example of a compact experimental setup.
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| | |
| A [[tuning fork]] can be held near the mouth of a long [[pipe (material)|pipe]] which is dipping into a barrel of [[water]]. 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+2n}λ/4)'' where ''n'' is an integer. As the [[antinode|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.
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| | |
| Here it is the case that ''v'' = ''fλ''
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| | |
| ==Non-gaseous media==
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| | |
| ===Speed of sound in solids===
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| | |
| ====Three-dimensional solids====
| |
| In a solid, there is a non-zero stiffness both for [[volumetric]] and shear deformations. Hence, it is possible to generate sound waves with different velocities dependent
| |
| on the deformation mode. Sound waves generating volumetric deformations (compressions) and shear deformations are called longitudinal waves and shear waves, respectively. In [[earthquake]]s, the corresponding seismic waves are called [[P-wave]]s and [[S-wave]]s, respectively. The sound velocities of these two types of waves propagating in a homogeneous 3-dimensional solid are respectively given by:<ref name="E. Kinsler 2000">L. E. Kinsler et al. (2000), ''Fundamentals of acoustics'', 4th Ed., John Wiley and sons Inc., New York, USA</ref>
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| | |
| <math> c_{\mathrm{p}} = \sqrt {\frac{K+\frac{4}{3}G}{\rho}} = \sqrt {\frac{Y (1-\nu)}{\rho (1+\nu)(1 - 2 \nu)}} </math>
| |
| | |
| <math> c_{\mathrm{s}} = \sqrt {\frac{G}{\rho}} </math>
| |
| | |
| where ''K'' and ''G'' are the [[bulk modulus]] and [[shear modulus]] of the elastic materials, respectively, ''Y'' is the [[Young's modulus]], <math>\rho</math> is the density, and <math>\nu</math> is [[Poisson's ratio]]. The last quantity is not an independent one, as <math>Y = 3K(1-2\nu)</math>. Note that the speed of longitudinal/compression waves depends both on the compression and shear resistance properties of the material, while the speed of shear waves depends on the shear properties only.
| |
| | |
| Typically, compression or P-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, ''K'' = 170 GPa, ''G'' = 80 GPa and <math> \rho </math> = 7700 kg/m<sup>3</sup>, yielding a longitudinal velocity ''c''<sub>l</sub> of
| |
| 6000 m/s.<ref name="E. Kinsler 2000"/>
| |
| This is in reasonable agreement with ''c''<sub>l</sub>=5930 m/s measured experimentally for a (possibly different) type of steel.<ref>J. Krautkrämer and H. Krautkrämer (1990), ''Ultrasonic testing of materials'', 4th fully revised edition,
| |
| Springer-Verlag, Berlin, Germany, p. 497</ref>
| |
| | |
| The [[shear velocity]] ''c''<sub>s</sub> is estimated at 3200 m/s using the same numbers.
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| | |
| ====Long rods====
| |
| The speed of sound for longitudinal waves in stiff materials such as metals is sometimes given for "long, thin 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 longitudinal waves may be simplified and is given by:
| |
| | |
| <math> c_{\mathrm{l}} = \sqrt {\frac{Y}{\rho}} </math>
| |
| | |
| This is similar to the expression for shear waves, save that [[Young's modulus]] replaces the [[shear modulus]]. This speed of sound for longitudinal waves in long, thin rods will always be slightly less than the 3-D, longitudinal wave speed in an isotropic materials, and the ratio of the speeds in the two different types of objects depends on [[Poisson's ratio]] for the material.
| |
| | |
| ===Speed of sound in liquids===
| |
| In a fluid the only non-zero [[stiffness]] is to volumetric deformation (a fluid does not sustain shear forces).
| |
| | |
| Hence the speed of sound in a fluid is given by
| |
| :<math>
| |
| c_{\mathrm{fluid}} = \sqrt {\frac{K}{\rho}}
| |
| </math>
| |
| | |
| where {{math|K}} is the [[bulk modulus]] of the fluid. This value typically decreases with temperature for non-polar fluids: the speed of sound in [[ultrawave|ultra-wave]] frequency range is inverse proportional to the cube of the volume of a fixed amount of the fluid.<ref>{{cite journal|last=Padmini|first=P. R. K. L.|coauthors=Ramachandra Rao|title=Molar Sound Velocity in Molten Hydrated Salts|journal=Nature|date=12 August 1961|volume=191|issue=4789|pages=694–695|doi=10.1038/191694a0|url=http://www.nature.com/nature/journal/v191/n4789/abs/191694a0.html|accessdate=10 February 2012|bibcode = 1961Natur.191..694P }}</ref>
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| | |
| ====Water====
| |
| The speed of sound in water is of interest to anyone using [[underwater acoustics|underwater sound]] as a tool, whether in a laboratory, a lake or the ocean. Examples are [[sonar]], [[Underwater acoustics#Underwater communication|acoustic communication]] and [[acoustical oceanography]]. See [http://www.dosits.org/ Discovery of Sound in the Sea] for other examples of the uses of sound in the ocean (by both man and other animals). In fresh water, sound travels at about 1497 m/s at 25 °C. See [http://www.npl.co.uk/acoustics/techguides/soundpurewater/ Technical Guides - Speed of Sound in Pure Water] for an online calculator.
| |
| | |
| ====Seawater====
| |
| [[File:SOFAR.png|thumb|200px|Sound speed 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]] is centered on the minimum in sound speed at ca. 750-m depth.]]
| |
| In salt water that is free of air bubbles or suspended sediment, sound travels at about 1560 m/s. The speed of sound in seawater depends on pressure (hence depth), temperature (a change of 1 °C ~ 4 m/s), and [[salinity]] (a
| |
| change of 1[[Per mil|‰]] ~ 1 m/s), and empirical equations have been derived to accurately calculate sound speed from these variables.<ref>[http://handle.dtic.mil/100.2/ADB199453 APL-UW TR 9407 High-Frequency Ocean Environmental Acoustic Models Handbook], pp. I1-I2.</ref> Other factors affecting sound speed are minor. Since temperature decreases with depth while pressure and generally salinity increase, the profile of sound speed with depth generally shows a characteristic curve which decreases to a minimum at a depth of several hundred meters, then increases again with increasing depth (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 |accessdate=2010-11-30}}</ref> For more information see Dushaw et al.<ref name=Dushaw93/>
| |
| | |
| A simple empirical equation for the speed of sound in sea water with reasonable accuracy for the world's oceans is due to Mackenzie:<ref>{{cite journal
| |
| | author = Mackenzie, Kenneth V.
| |
| | 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>
| |
| :''c''(''T'', ''S'', ''z'') = ''a''<sub>1</sub> + ''a''<sub>2</sub>''T'' + ''a''<sub>3</sub>''T''<sup>2</sup> + ''a''<sub>4</sub>''T''<sup>3</sup> + ''a''<sub>5</sub>(''S'' - 35) + ''a''<sub>6</sub>''z'' + ''a''<sub>7</sub>''z''<sup>2</sup> + ''a''<sub>8</sub>''T''(''S'' - 35) + ''a''<sub>9</sub>''Tz''<sup>3</sup>
| |
| where ''T'', ''S'', and ''z'' are temperature in degrees Celsius, salinity in parts per thousand and depth in meters, respectively. The constants ''a''<sub>1</sub>, ''a''<sub>2</sub>, ..., ''a''<sub>9</sub> are:
| |
| :''a''<sub>1</sub> = 1448.96, ''a''<sub>2</sub> = 4.591, ''a''<sub>3</sub> = -5.304×10<sup>-2</sup>, ''a''<sub>4</sub> = 2.374×10<sup>-4</sup>, ''a''<sub>5</sub> = 1.340, <br>''a''<sub>6</sub> = 1.630×10<sup>-2</sup>, ''a''<sub>7</sub> = 1.675×10<sup>-7</sup>, ''a''<sub>8</sub> = -1.025×10<sup>-2</sup>, ''a''<sub>9</sub> = -7.139×10<sup>-13</sup>
| |
| with check value 1550.744 m/s for ''T''=25 °C, ''S''=35 parts per thousand, ''z''=1000 m. This equation has a standard error of 0.070 m/s for salinity between 25 and 40 [[Parts per thousand|ppt]]. See [http://www.npl.co.uk/acoustics/techguides/soundseawater/ Technical Guides - Speed of Sound in Sea-Water] for an online calculator.
| |
| | |
| Other equations for sound speed 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
| |
| | author = Del Grosso, 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 }}</ref> and the Chen-Millero-Li Equation.<ref name=Dushaw93>{{cite journal
| |
| | last = Dushaw |first = Brian D.
| |
| | coauthors = Worcester, P.F.; Cornuelle, B.D.; and Howe, 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
| |
| | last = Meinen | first = Christopher S.
| |
| | coauthors = Watts, 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 }}</ref>
| |
| | |
| ===Speed 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 [[Plasma parameters#Velocities|here]])
| |
| :<math>
| |
| c_s = (\gamma ZkT_e/m_i)^{1/2} = 9.79\times10^3\,(\gamma ZT_e/\mu)^{1/2}\,\mbox{m/s}\,
| |
| </math>
| |
| | |
| where <math>m_i</math> is the [[ion]] mass, <math>\mu</math> is the ratio of ion mass to [[proton]] mass <math>\mu = m_i/m_p</math>; <math>T_e</math> is the [[electron]] temperature; ''Z'' is the charge state; ''k'' is [[Boltzmann's constant]]; ''K'' is wavelength; and <math>\gamma</math> 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.
| |
| | |
| ==Gradients==
| |
| {{main|sound speed gradient}}
| |
| 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 higher [[refractive index|index]], sound waves will [[refraction|refract]] 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 in a sheet of glass or [[optical fiber]]. 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]] at a considerable distance.
| |
| | |
| ==See also==
| |
| *[[Elastic wave]]
| |
| *[[Second sound]]
| |
| *[[Sonic boom]]
| |
| *[[Sound barrier]]
| |
| *[[Underwater acoustics]]
| |
| *[[Vibrations]]
| |
| | |
| ==References==
| |
| {{Reflist|colwidth=30em}}
| |
| | |
| ==External links==
| |
| *[http://www.sengpielaudio.com/calculator-speedsound.htm Calculation: Speed of sound in air and the temperature]
| |
| *[http://www.sengpielaudio.com/SpeedOfSoundPressure.pdf Speed of sound - temperature matters, not air pressure]
| |
| *[http://www.pdas.com/atmos.html Properties Of The U.S. Standard Atmosphere 1976]
| |
| *[http://www.mathpages.com/home/kmath109/kmath109.htm The Speed of Sound]
| |
| *[http://www.bustertests.co.uk/answer/how-to-measure-the-speed-of-sound-in-a-laboratory/ How to measure the speed of sound in a laboratory]
| |
| *[http://www.acoustics.salford.ac.uk/schools/index1.htm Teaching resource for 14-16 yrs on sound including speed of sound]
| |
| *[http://www.npl.co.uk/acoustics/techguides/soundpurewater/ Technical Guides - Speed of Sound in Pure Water]
| |
| *[http://www.npl.co.uk/acoustics/techguides/soundseawater/ Technical Guides - Speed of Sound in Sea-Water]
| |
| *[http://space.newscientist.com/article/mg19826504.200-did-sound-once-travel-at-light-speed.html?feedId=online-news_rss20 Did sound once travel at light speed?]
| |
| *[http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Reference%20Information/matproperties.htm Acoustic properties of various materials including sound speed]
| |
| * [http://scholar.google.com/citations?user=hZvL5eYAAAAJ&hl=en Sameen Ahmed Khan], [http://indapt.org/images/stories/bulletin2012/bulletin_may_2012.pdf Speed of Sound in Air at varying Temperatures], Bulletin of the IAPT, Volume 4, No. 5, 116-117 (May 2012). (Publication of the [[Indian Association of Physics Teachers]]).
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| {{Use dmy dates|date=May 2011}}
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| {{DEFAULTSORT:Speed Of Sound}}
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| [[Category:Aerodynamics]]
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| [[Category:Chemical properties]]
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| [[Category:Fluid dynamics]]
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| [[Category:Sound measurements]]
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| [[Category:Units of velocity]]
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