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Speed of sound
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For other uses, see Speed of sound (disambiguation).
Sound measurements
Characteristic
Symbols
Sound pressure
p, SPL,LPA
Particle velocity
v, SVL
Particle displacement
δ
Sound intensity
I, SIL
Sound power
P, SWL, LWA
Sound energy
W
Sound energy density
w
Sound exposure
E, SEL
Acoustic impedance
Z
Speed of sound
c
Audio frequency
AF
Transmission loss
TL
v
t
e
The speed of sound is the distance travelled per unit time by a sound wave as it propagates through an elastic medium. In dry air at 0 °C (32 °F), the speed of sound is 331.2 metres per second (1,087 ft/s; 1,192 km/h; 741 mph; 644 kn). At 20 °C (68 °F), the speed of sound is 343 metres per second (1,125 ft/s; 1,235 km/h; 767 mph; 667 kn), or a kilometre in 2.91 s or a mile in 4.69 s.
The speed of sound in an ideal gas 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 common everyday speech, speed of sound refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance: sound travels most slowly in gases; it travels faster in liquids; and faster still in solids. For example, (as noted above), sound travels at 343 m/s in air; it travels at 1,484 m/s in water (4.3 times as fast as in air); and at 5,120 m/s in iron (about 15 times as fast as in air). In an exceptionally stiff material such as diamond, sound travels at 12,000 metres per second (26,843 mph);[1] (about 35 times as fast as in air) which is around the maximum speed that sound will 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, as exhibited in seismology. The speed of compression waves 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.
In fluid dynamics, 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 fluid is called the object's Mach number. Objects moving at speeds greater than Mach1 are said to be traveling at supersonic speeds.
Contents
[hide]
1 History
2 Basic concepts
2.1 Compression and shear waves
3 Equations
4 Dependence on the properties of the medium
5 Altitude variation and implications for atmospheric acoustics
6 Practical formula for dry air
7 Details
7.1 Speed of sound in ideal gases and air
7.2 Effects due to wind shear
7.3 Tables
8 Effect of frequency and gas composition
8.1 General physical considerations
8.2 Practical application to air
9 Mach number
10 Experimental methods
10.1 Single-shot timing methods
10.2 Other methods
10.3 High-precision measurements in air
11 Non-gaseous media
11.1 Speed of sound in solids
11.1.1 Three-dimensional solids
11.1.2 One-dimensional solids
11.2 Speed of sound in liquids
11.2.1 Water
11.2.2 Seawater
11.3 Speed of sound in plasma
12 Gradients
13 See also
14 References
15 External links
History[edit]
Sir Isaac Newton computed the speed of sound in air as 979 feet per second (298 m/s), which is too low by about 15%,[2]. Newton's analysis was good save for 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, not an isothermal process). This error was later rectified by Laplace.[3]
During the 17th century, there were several attempts to measure the speed of sound accurately, including attempts by Marin Mersenne 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).[4]
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.[4] 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, and thus the speed that the sound had travelled was calculated.[5]
Basic concepts[edit]
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 the stiffness/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. Effects like dispersion and reflection can also be understood using this model.[citation needed]
In a real material, the stiffness of the springs is known as the "elastic modulus", and the mass corresponds to the material density. Given that all other things being equal (ceteris paribus), sound will travel slower 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 (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.
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 levels 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.
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[edit]
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). A pressure-type wave may also travel in solids, along with other types of waves (transverse waves, see below)
Transverse wave affecting atoms initially confined to a plane. This additional type of sound wave (additional type of elastic wave) travels only in solids, for it requires a sideways shearing motion which is supported by the presence of elasticity in the solid. The sideways shearing motion may take place in any direction which is at right-angle 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
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, 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 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.
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 and density, but with the additional factor of shear modulus 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[edit]
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 = K s ρ , {\displaystyle c={\sqrt {\frac {K_{s}}{\rho }}},}
where
Ks is a coefficient of stiffness, the isentropic bulk modulus (or the modulus of bulk elasticity for gases);
ρ is the density.
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 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 is used, the speed of sound c is given by
c = ( ∂ p ∂ ρ ) s , {\displaystyle c={\sqrt {\left({\frac {\partial p}{\partial \rho }}\right)_{s}}},}
where
p is the pressure;
ρ is the density and the derivative is taken isentropically, that is, at constant entropy s.
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 CO2 which is a dispersive medium, and causes dispersion to air at ultrasonic frequencies (> 28 kHz).[6]
In a dispersive medium, the speed of sound is a function of sound frequency, through the dispersion relation. Each frequency component propagates at its own speed, called the phase velocity, while the energy of the disturbance propagates at the group velocity. The same phenomenon occurs with light waves; see optical dispersion for a description.
Dependence on the properties of the medium[edit]
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 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.
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 (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).
In low molecular weight gases such as helium, sound propagates faster as compared to heavier gases such as xenon. 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 the molecular composition is fixed, and thus the speed of sound depends only on its temperature. At a constant temperature, the gas pressure has no effect on the speed of sound, since the density will increase, and since 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 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 oxygen and nitrogen molecules of the air are replaced by lighter molecules of water. This is a simple mixing effect.
Altitude variation and implications for atmospheric acoustics[edit]
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 the speed of sound cancel each other. Speed of sound increases with height in two regions of the stratosphere and thermosphere, due to heating effects in these regions.
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, the speed of sound is dependent solely upon temperature; see 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.
Since temperature (and thus the speed of sound) decreases with increasing altitude up to 11 km, sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source.[7] 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 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 speed of sound gradient in this region. Still another region of positive gradient occurs at very high altitudes, in the aptly-named thermosphere above 90 km.
Practical formula for dry air[edit]
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Approximation of the speed of sound in dry air based on the heat capacity ratio (in green) against the truncated Taylor expansion (in red).
The approximate speed of sound in dry (0% humidity) air, in meters per second, at temperatures near 0 °C, can be calculated from
c a i r = ( 331.3 + 0.606 ⋅ ϑ ) m / s , {\displaystyle c_{\mathrm {air} }=(331.3+0.606\cdot \vartheta )~~~\mathrm {m/s} ,}
where ϑ {\displaystyle \vartheta } is the temperature in degrees Celsius (°C).
This equation is derived from the first two terms of the Taylor expansion of the following more accurate equation:
c a i r = 331.3 1 + ϑ 273.15 m / s . {\displaystyle c_{\mathrm {air} }=331.3~{\sqrt {1+{\frac {\vartheta }{273.15}}}}~~~~\mathrm {m/s} .}
Dividing the first part, and multiplying the second part, on the right hand side, by √273.15 gives the exactly equivalent form
c a i r = 20.05 ϑ + 273.15 m / s . {\displaystyle c_{\mathrm {air} }=20.05~{\sqrt {\vartheta +273.15}}~~~~\mathrm {m/s} .}
which can also be written as
c a i r = 20.05 T / K m / s {\displaystyle c_{\mathrm {air} }=20.05~{\sqrt {T/K}}~~~~\mathrm {m/s} }
where T denotes the thermodynamic temperature.
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, γ, as well as on the fact that at 1 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 γ 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.
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.
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.
Details[edit]
Speed of sound in ideal gases and air[edit]
For an ideal gas, K (the bulk modulus in equations above, equivalent to C, the coefficient of stiffness in solids) is given by
K = γ ⋅ p , {\displaystyle K=\gamma \cdot p,}
thus, from the Newton–Laplace equation above, the speed of sound in an ideal gas is given by
c = γ ⋅ p ρ , {\displaystyle c={\sqrt {\gamma \cdot {p \over \rho }}},}
where
γ 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( C p / C v {\displaystyle 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;
ρ is the density.
Using the ideal gas law to replace p with nRT/V, and replacing ρ with nM/V, the equation for an ideal gas becomes
c i d e a l = γ ⋅ p ρ = γ ⋅ R ⋅ T M = γ ⋅ k ⋅ T m , {\displaystyle 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}},}
where
cideal is the speed of sound in an ideal gas;
R (approximately 8.314,5 J · mol−1 · K−1) is the molar gas constant(universal gas constant);[8]
k is the Boltzmann constant;
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 7/5 = 1.400 for diatomic molecules, according to kinetic theory. Gamma is actually experimentally measured over a range from 1.399,1 to 1.403 at 0 °C, for air. Gamma is exactly 5/3 = 1.6667 for monatomic gases such as noble gases;
T is the absolute temperature;
M is the molar mass of the gas. The mean molar mass for dry air is about 0.028,964,5 kg/mol;[citation needed]
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 cair have been found to vary slightly from experimentally determined values.[9]
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 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 γ = 1.4000 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 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 a i r . {\displaystyle R_{*}=R/M_{\mathrm {air} }.}
In addition, we switch to the Celsius temperature ϑ {\displaystyle \vartheta } = T − 273.15, which is useful to calculate air speed in the region near 0°C (about 273 kelvin). Then, for dry air,
c i d e a l = γ ⋅ R ∗ ⋅ T = γ ⋅ R ∗ ⋅ ( ϑ + 273.15 ) , {\displaystyle c_{\mathrm {ideal} }={\sqrt {\gamma \cdot R_{*}\cdot T}}={\sqrt {\gamma \cdot R_{*}\cdot (\vartheta +273.15)}},}
c i d e a l = γ ⋅ R ∗ ⋅ 273.15 ⋅ 1 + ϑ 273.15 , {\displaystyle c_{\mathrm {ideal} }={\sqrt {\gamma \cdot R_{*}\cdot 273.15}}\cdot {\sqrt {1+{\frac {\vartheta }{273.15}}}},}
where ϑ {\displaystyle \vartheta } (theta) is the temperature in degrees Celsius(°C).
Substituting numerical values
R = 8.314 510 J / ( m o l ⋅ K ) {\displaystyle R=8.314\,510~\mathrm {J/(mol\cdot K)} }
for the molar gas constant in J/mole/Kelvin, and
M a i r = 0.028 964 5 k g / m o l {\displaystyle M_{\mathrm {air} }=0.028\,964\,5~\mathrm {kg/mol} }
for the mean molar mass of air, in kg; and using the ideal diatomic gas value of γ = 1.4000, we have
c a i r = 331.3 1 + ϑ 273.15 m / s . {\displaystyle c_{\mathrm {air} }=331.3~~{\sqrt {1+{\frac {\vartheta }{273.15}}}}~~~\mathrm {m/s} .}
Finally, Taylor expansion of the remaining square root in ϑ {\displaystyle \vartheta } yields
c a i r = 331.3 ( 1 + ϑ 2 ⋅ 273.15 ) m / s , {\displaystyle c_{\mathrm {air} }=331.3~(1+{\frac {\vartheta }{2\cdot 273.15}})~~~\mathrm {m/s} ,}
c a i r = ( 331.3 + 0.606 ⋅ ϑ ) m / s . {\displaystyle c_{\mathrm {air} }=(331.3+0.606\cdot \vartheta )~~~\mathrm {m/s} .}
The above derivation includes the first two equations given in the "Practical formula for dry air" section above.
Effects due to wind shear[edit]
The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source.[7] Wind shear of 4 m/(s · km) can produce refraction equal to a typical temperature lapse rate of 7.5 °C/km.[10] Higher values of wind gradient will refract sound downward toward the surface in the downwind direction,[11] 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.[12]
For sound propagation, the exponential variation of wind speed with height can be defined as follows:[13]
U ( h ) = U ( 0 ) h ζ , {\displaystyle U(h)=U(0)h^{\zeta },}
d U d H ( h ) = ζ U ( h ) h , {\displaystyle {\frac {\mathrm {d} U}{\mathrm {d} H}}(h)=\zeta {\frac {U(h)}{h}},}
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 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,[14] because they could not hear the sounds of battle only 10 km (six miles) downwind.[15]
Tables[edit]
In the standard atmosphere:
T0 is 273.15 K (= 0 °C = 32 °F), giving a theoretical value of 331.3 m/s (= 1086.9 ft/s = 1193 km/h = 741.1 mph = 644.0 kn). Values ranging from 331.3 to 331.6 m/s may be found in reference literature, however;
T20 is 293.15 K (= 20 °C = 68 °F), giving a value of 343.2 m/s (= 1126.0 ft/s = 1236 km/h = 767.8 mph = 667.2 kn);
T25 is 298.15 K (= 25 °C = 77 °F), giving a value of 346.1 m/s (= 1135.6 ft/s = 1246 km/h = 774.3 mph = 672.8 kn).
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.
Effect of temperature on properties of air
Temperature
T (°C)
Speed of sound
c (m/s)
Density of air
ρ (kg/m3)
Characteristic specific acoustic impedance
z0 (Pa·s/m)
35 351.88 1.1455 403.2
30 349.02 1.1644 406.5
25 346.13 1.1839 409.4
20 343.21 1.2041 413.3
15 340.27 1.2250 416.9
10 337.31 1.2466 420.5
5 334.32 1.2690 424.3
0 331.30 1.2922 428.0
−5 328.25 1.3163 432.1
−10 325.18 1.3413 436.1
−15 322.07 1.3673 440.3
−20 318.94 1.3943 444.6
−25 315.77 1.4224 449.1
Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:
Altitude Temperature m/s km/h mph kn
Sea level 15 °C (59 °F) 340 1,225 761 661
11,000 m−20,000 m
(Cruising altitude of commercial jets,
and first supersonic flight) −57 °C (−70 °F) 295 1,062 660 573
29,000 m (Flight of X-43A) −48 °C (−53 °F) 301 1,083 673 585
Effect of frequency and gas composition[edit]
General physical considerations[edit]
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.[16]
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.[9] 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.
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 (5/3 = 1.66…) than diatomics do (7/5 = 1.4). Thus, at the same molecular mass, the speed of sound of a monatomic gas goes up by a factor of
c g a s , m o n a t o m i c c g a s , d i a t o m i c = 5 / 3 7 / 5 = 25 21 = 1.091 … {\displaystyle {c_{\mathrm {gas,monatomic} } \over c_{\mathrm {gas,diatomic} }}={\sqrt {{5/3} \over {7/5}}}={\sqrt {25 \over 21}}=1.091\ldots }
This gives the 9% difference, and would be a typical ratio for speeds of sound 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 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). 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 the speed of sound in monatomic vs. polyatomic molecules, with the speed remaining greater in monatomics.
Practical application to air[edit]
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 0.6 m/s 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 but decreased by carbon dioxide. The difference between 0% and 100% humidity is about 1.5 m/s at standard pressure and temperature, but the size of the humidity effect increases dramatically with temperature. The carbon dioxide content of air is not fixed, due to both carbon pollution and human breath (e.g., in the air blown through wind instruments).
The dependence on frequency and pressure are normally insignificant in practical applications. In dry air, the speed of sound increases by about 0.1 m/s as the frequency rises from 10 Hz to 100 Hz. For audible frequencies above 100 Hz 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.[17]
Mach number[edit]
Main article: Mach number
U.S. Navy 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).[18]
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.
Experimental methods[edit]
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 by Isaac Newton. Derham had a telescope at the top of the tower of the 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 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 meters, and not needing something as loud as a shotgun.
Single-shot timing methods[edit]
The simplest concept is the measurement made using two microphones 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[edit]
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 nodes and antinodes visible to the human eye. This is an example of a compact experimental setup.
A tuning fork can be held near the mouth of a long 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 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[edit]
The effect from 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[19] 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 30 °C but corrected for temperature in order to report them at 0 °C. The result was 331.45 ± 0.01 m/s for dry air at STP, for frequencies from 93 Hz to 1,500 Hz.
Non-gaseous media[edit]
Speed of sound in solids[edit]
Three-dimensional solids[edit]
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. In earthquakes, the corresponding seismic waves are called P-waves (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 by[20]
c s o l i d , p = K + 4 3 G ρ = E ( 1 − ν ) ρ ( 1 + ν ) ( 1 − 2 ν ) , {\displaystyle c_{\mathrm {solid,p} }={\sqrt {\frac {K+{\frac {4}{3}}G}{\rho }}}={\sqrt {\frac {E(1-\nu )}{\rho (1+\nu )(1-2\nu )}}},}
c s o l i d , s = G ρ , {\displaystyle c_{\mathrm {solid,s} }={\sqrt {\frac {G}{\rho }}},}
where
K is the bulk modulus of the elastic materials;
G is the shear modulus of the elastic materials;
E is the Young's modulus;
ρ is the density;
ν is Poisson's ratio.
The last quantity is not an independent one, as E = 3K(1 − 2ν). 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, K = 170 GPa, G = 80 GPa and ρ = 7,700 kg/m3, yielding a compressional speed csolid,p of 6,000 m/s.[20] This is in reasonable agreement with csolid,p measured experimentally at 5,930 m/s for a (possibly different) type of steel.[21] The shear speed csolid,s is estimated at 3,200 m/s using the same numbers.
One-dimensional solids[edit]
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 s o l i d = E ρ , {\displaystyle c_{\mathrm {solid} }={\sqrt {\frac {E}{\rho }}},}
where E is Young's modulus. This is similar to the expression for shear waves, save that Young's modulus replaces the shear modulus. 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.
Speed of sound in liquids[edit]
Speed of sound in water vs temperature.
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
c f l u i d = K ρ , {\displaystyle c_{\mathrm {fluid} }={\sqrt {\frac {K}{\rho }}},}
where K is the bulk modulus of the fluid.
Water[edit]
In fresh water, sound travels at about 1481 m/s at 20 °C (see the External Links section below for online calculators).[22] Applications of underwater sound can be found in sonar, acoustic communication and acoustical oceanography.
Seawater[edit]
See also: Sound speed profile
Speed of sound as a function of depth at a position north of Hawaii in the Pacific Ocean derived from the 2005 World Ocean Atlas. The SOFAR channel is centred on the minimum in the speed of sound at ca. 750-m depth.
In salt water that is free of air bubbles or suspended sediment, sound travels at about 1500 m/s (1500.235 m/s at 1000 kilopascals, 10 °C and 3% salinity by one method).[23] 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‰ ~ 1 m/s), and empirical equations have been derived to accurately calculate the speed of sound from these variables.[24][25] Other factors affecting the speed of sound are minor. Since temperature decreases with depth while pressure and generally salinity increase, the profile of the speed of sound 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).[26] For more information see Dushaw et al.[27]
A simple empirical equation for the speed of sound in sea water with reasonable accuracy for the world's oceans is due to Mackenzie:[28]
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 , {\displaystyle 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}Tz^{3},}
where
T is the temperature in degrees Celsius;
S is the salinity in parts per thousand;
z is the depth in meters.
The constants a1, a2, …, a9 are
a 1 = 1 , 448.96 , a 2 = 4.591 , a 3 = − 5.304 × 10 − 2 , a 4 = 2.374 × 10 − 4 , a 5 = 1.340 , a 6 = 1.630 × 10 − 2 , a 7 = 1.675 × 10 − 7 , a 8 = − 1.025 × 10 − 2 , a 9 = − 7.139 × 10 − 13 , {\displaystyle {\begin{aligned}a_{1}&=1,448.96,&a_{2}&=4.591,&a_{3}&=-5.304\times 10^{-2},\\a_{4}&=2.374\times 10^{-4},&a_{5}&=1.340,&a_{6}&=1.630\times 10^{-2},\\a_{7}&=1.675\times 10^{-7},&a_{8}&=-1.025\times 10^{-2},&a_{9}&=-7.139\times 10^{-13},\end{aligned}}}
with check value 1550.744 m/s for T = 25 °C, S = 35 parts per thousand, z = 1,000 m. This equation has a standard error of 0.070 m/s for salinity between 25 and 40 ppt. See Technical Guides. Speed of Sound in Sea-Water for an online calculator.
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[29] and the Chen-Millero-Li Equation.[27][30]
Speed of sound in plasma[edit]
The speed of sound in a 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 = ( γ Z k T e / m i ) 1 / 2 = 9.79 × 10 3 ( γ Z T e / μ ) 1 / 2 m / s , {\displaystyle c_{s}=(\gamma ZkT_{\mathrm {e} }/m_{\mathrm {i} })^{1/2}=9.79\times 10^{3}(\gamma ZT_{e}/\mu )^{1/2}~\mathrm {m/s} ,}
where
mi is the ion mass;
μ is the ratio of ion mass to proton mass μ = mi/mp;
Te is the electron temperature;
Z is the charge state;
k is Boltzmann constant;
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.
Gradients[edit]
Main article: 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 index, sound waves will 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[edit]
Acoustoelastic effect
Elastic wave
Second sound
Sonic boom
Sound barrier
Underwater acoustics
Vibrations
References[edit]
Jump up ^ Speed of Sound
Jump up ^ "The Speed of Sound". mathpages.com. Retrieved 3 May 2015.
Jump up ^ Bannon, Mike; Kaputa, Frank. "The Newton–Laplace Equation and Speed of Sound". Thermal Jackets. Retrieved 3 May 2015.
^ Jump up to: a b Murdin, Paul (25 December 2008). Full Meridian of Glory: Perilous Adventures in the Competition to Measure the Earth. Springer Science & Business Media. pp. 35–36. ISBN 9780387755342.
Jump up ^ Fox, Tony (2003). Essex Journal. Essex Arch & Hist Soc. pp. 12–16.
Jump up ^ Dean, E. A. (August 1979). Atmospheric Effects on the Speed of Sound, Technical report of Defense Technical Information Center
^ Jump up to: a b Everest, F. (2001). The Master Handbook of Acoustics. New York: McGraw-Hill. pp. 262–263. ISBN 0-07-136097-2.
Jump up ^ "CODATA Value: molar gas constant". Physics.nist.gov. Retrieved 24 October 2010.
^ Jump up to: a b U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976.
Jump up ^ Uman, Martin (1984). Lightning. New York: Dover Publications. ISBN 0-486-64575-4.
Jump up ^ Volland, Hans (1995). Handbook of Atmospheric Electrodynamics. Boca Raton: CRC Press. p. 22. ISBN 0-8493-8647-0.
Jump up ^ Singal, S. (2005). Noise Pollution and Control Strategy. Oxford: Alpha Science International. p. 7. ISBN 1-84265-237-0. 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.
Jump up ^ Bies, David (2004). Engineering Noise Control, Theory and Practice. London: Spon Press. p. 235. ISBN 0-415-26713-7. 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.
Jump up ^ Cornwall, Sir (1996). Grant as Military Commander. New York: Barnes & Noble. p. 92. ISBN 1-56619-913-1.
Jump up ^ Cozens, Peter (2006). The Darkest Days of the War: the Battles of Iuka and Corinth. Chapel Hill: The University of North Carolina Press. ISBN 0-8078-5783-1.
Jump up ^ A B Wood, A Textbook of Sound (Bell, London, 1946)
Jump up ^ "Speed of Sound in Air". Phy.mtu.edu. Retrieved 13 June 2014.
Jump up ^ Nemiroff, R.; Bonnell, J., eds. (19 August 2007). "A Sonic Boom". Astronomy Picture of the Day. NASA. Retrieved 24 October 2010.
Jump up ^ Zuckerwar, Handbook of the speed of sound in real gases, p. 52
^ Jump up to: a b L. E. Kinsler et al. (2000), Fundamentals of acoustics, 4th Ed., John Wiley and sons Inc., New York, USA.
Jump up ^ J. Krautkrämer and H. Krautkrämer (1990), Ultrasonic testing of materials, 4th fully revised edition, Springer-Verlag, Berlin, Germany, p. 497
Jump up ^ "Speed of Sound in Water at Temperatures between 32–212 oF (0–100 oC) — imperial and SI units". The Engineering Toolbox.
Jump up ^ Wong, George S. K.; Zhu, Shi-ming (1995). "Speed of sound in seawater as a function of salinity, temperature, and pressure". The Journal of the Acoustical Society of America. 97 (3): 1732. Bibcode:1995ASAJ...97.1732W. doi:10.1121/1.413048.
Jump up ^ APL-UW TR 9407 High-Frequency Ocean Environmental Acoustic Models Handbook, pp. I1-I2.
Jump up ^ Robinson, Stephen (22 Sep 2005). "Technical Guides - Speed of Sound in Sea-Water". National Physical Laboratory. Retrieved 7 December 2016.
Jump up ^ "How Fast Does Sound Travel?". Discovery of Sound in the Sea. University of Rhode Island. Retrieved 30 November 2010.
^ Jump up to: a b Dushaw, Brian D.; Worcester, P. F.; Cornuelle, B. D.; Howe, B. M. (1993). "On Equations for the Speed of Sound in Seawater". Journal of the Acoustical Society of America. 93 (1): 255–275. Bibcode:1993ASAJ...93..255D. doi:10.1121/1.405660.
Jump up ^ Kenneth V., Mackenzie (1981). "Discussion of sea-water sound-speed determinations". Journal of the Acoustical Society of America. 70 (3): 801–806. Bibcode:1981ASAJ...70..801M. doi:10.1121/1.386919.
Jump up ^ Del Grosso, V. A. (1974). "New equation for speed of sound in natural waters (with comparisons to other equations)". Journal of the Acoustical Society of America. 56 (4): 1084–1091. Bibcode:1974ASAJ...56.1084D. doi:10.1121/1.1903388.
Jump up ^ Meinen, Christopher S.; Watts, D. Randolph (1997). "Further Evidence that the Sound-Speed Algorithm of Del Grosso Is More Accurate Than that of Chen and Millero". Journal of the Acoustical Society of America. 102 (4): 2058–2062. Bibcode:1997ASAJ..102.2058M. doi:10.1121/1.419655.
External links[edit]
Calculation: Speed of Sound in Air and the Temperature
Speed of sound: Temperature Matters, Not Air Pressure
Properties of the U.S. Standard Atmosphere 1976
The Speed of Sound
How to Measure the Speed of Sound in a Laboratory
Teaching Resource for 14-16 Years on Sound Including Speed of Sound
Technical Guides. Speed of Sound in Pure Water
Technical Guides. Speed of Sound in Sea-Water
Did Sound Once Travel at Light Speed?
Acoustic Properties of Various Materials Including the Speed of Sound
Technical Guides - Speed of Sound in Pure Water (provides a calculator for the speed in water)
Discovery of Sound in the Sea (uses of sound by humans and other animals)
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Vehicle registration plates of Europe
From Wikipedia, the free encyclopedia
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It has been suggested that Vehicle registration plates of the European Union be merged into this article. (Discuss) Proposed since June 2017.
This article is about registration plates of Europe. For registration plates of members of the European Union, which share a common format, see Vehicle registration plates of the European Union.
The common EU format.
(A denotes Austria).
Norwegian implementation of a format similar to the EU format. Both formats satisfy the Vienna Convention on road traffic.
Turkish implementation of a format similar to the EU format. The circle of stars is removed, but no national symbol is added.
A European vehicle registration plate is a vehicle registration plate, a metal or plastic plate or plates attached to a motor vehicle or trailer for official identification purposes. The registration identifier is a numeric or alphanumeric code that uniquely identifies the vehicle within the issuing authority's database. In Europe most countries have adopted a common format for number plates, such as the common EU format issued in EU member states. This format satisfies the requirements in the Vienna Convention on Road Traffic, which states that cross-border vehicles must display a distinguishing code for the country of registration on the rear of the vehicle. This sign may either be an oval sticker placed separately from the registration plate or may be incorporated into the vehicle registration plate. When the distinguishing sign is incorporated into the registration plate, it must also appear on the front registration plate of the vehicle, and may be supplemented with the flag or emblem of the national state, or the emblem of the regional economic integration organization to which the country belongs.[1]
Contents
[hide]
1 Format
1.1 Common letter and digit systems between countries
1.2 Differing numbering systems
2 Cross-border traffic
2.1 Countries
2.2 Dependencies, partially recognized and disputed territories
3 List
3.1 Countries [8]
3.2 Dependencies, partially recognized and disputed territories
3.3 Motorcycle plates
3.4 Countries
3.5 Dependencies, partially recognized and disputed territories
4 See also
5 Notes and references
6 External links
Format[edit]
The common EU format of having a blue section on the extreme left with EU circle of stars and the country code was introduced by Council Regulation (EC) No 2411/98 of 3 November 1998[2] and entered into force on the 11 November 1998. It was based on a model registration plate which three member states had already introduced before: Ireland (1991),[3] Portugal (1992) [4] and Germany (1994).[5] Luxembourg plates had displayed the European Flag on the left part since 1988.
The common design consists of a blue strip on the left side of the plate. This blue strip has the European flag symbol (twelve yellow stars), along with the country code of the member state in which the vehicle is registered. Danish plates have a small holographic strip to the right of the blue EU strip.
EU format plates are either white or yellow, on a plate wider than it is tall. Yellow registration plates are used both front and rear in Luxembourg and the Netherlands. In Gibraltar, the United Kingdom and Cyprus, yellow plates are used at the rear and white at the front. The UK use flat plastic plates (embossed metal plates are an option in the UK), as opposed to metal plates in most other European countries. A mixture of plastic or metal plates is permitted in France and Ireland. Plastic plates have earlier also been used in Sweden and Norway
Denmark and Hungary use yellow plates for vehicles registered as commercial vehicles and in Greece, Latvia, Lithuania and Sweden yellow plates are used for taxi vehicles. Belgium uses red characters and is the only country not to use the standard black-on-white or black-on-yellow combination; with the introduction of European-style plates in November 2010, a slightly darker shade of red was chosen (RAL 3003) to improve legibility. In Norway, cars with front seats only (used for cargo) have green plates with black characters.
The EU format is optional in Denmark,[6] Finland, the United Kingdom and also Cyprus. This is because of the way in which the Council Regulation implementing the EU Symbol (Regulation No. 2411/98) is drafted. It only requires states that have ratified the Vienna Convention of 1968 on road traffic to enforce the EU symbol.
Several non-EU European states have implemented similar formats, replacing the circle of stars with own symbols. Norway is an example of such state, issuing europlates with the Norwegian flag replacing the circle of stars. Iceland issues plates with the Icelandic flag above the country code on the left side. From those states that joined in the 2004 enlargement of the European Union Malta already used europlates, while Latvia, Poland and Lithuania had used EU number plates displaying the national flag before their accession, as did Bulgaria and Romania before their accession in 2007.
Turkey is not a member of the EU, however uses the blue European strip on the left of the plate as a member of European Customs Union (only member of the union without EU membership), with the country code (TR), but without the 12-EU stars sign. License plates consist of letters and digits in combinations of 99 AB 999, 99 A 9999, 99 ABC 99, 99 AB 9999 or 99 A 99999 where the first two digits show which province the vehicle is registered from. First two digits numbers go from 01 to 81 (as there are 81 provinces in Turkey) and each one is assigned to a province with alphabetical order e.g. 01 is the code of the province Adana or 34 is the code of the province Istanbul. All 81 provinces uses "01 AB 123" style plates initially until all combinations ran out, then the province starts to use 01 A 1234 then 01 ABC 12 etc. As a result, three largest provinces i.e. Istanbul, Ankara and İzmir are currently issuing 99 AB 9999 style plates since they used all combinations of previous series but the province Sivas for example, still issues 99 AB 999 plates as having a modest population and number of vehicles. 99 A 99999 series are not regular since they are only used in provinces where commercial vehicles are abundant e.g. Bursa to distinguish these vehicles there from passenger cars. Letters "I" and "O" are only used in the middle 01 ABC 12 series e.g. 34 YOC 34 or 06 TIL 56 to avoid confusion with numerals "1" and "0" respectively. Also some letters combinations like "PKK" are not issued due to their referring to political organizations or words likely to cause offence.
Common letter and digit systems between countries[edit]
Several countries have made efforts to avoid duplicating registration numbers used by other countries. Nevertheless, this is not completely successful and there are occasional difficulties for example in connection with parking fines and automatic speed cameras.
Belgium (until 2010), Cyprus, Finland, Georgia (until 2014), Hungary, Lithuania, Malta, Sweden (since 1974), and Moldova (since 2014) each use combinations of first three letters and then three digits.
Bulgaria uses plate numbers in the form A[A]-0000-A[A], i.e. one or two letters representing the region, then four digits, then one or two more letters. All letters used are intersection of Latin and Cyrillic alphabet, i.e. A, B, C, E, H, K, M, O, P, T, X and Y.
Greece uses a combination of three letters (which are the intersection of Latin and Greek alphabet, i.e. A, B, E, Z, H, I, K, M, N, O, P, T, Y, X in Greek alphabetic order) and four numbers, in the form of AAA-0000, while Spain uses a four number-three letter combination, in the form of 0000 BBB (vowels and some maybe confusing consonants, like Ñ and Q, are not used)
Denmark and Norway use two letters and five digits (for trailers in Denmark two letters but just four digits). The plates look very similar, but Denmark has a red border around the plate. Use of the country code on the plate may mitigate this problem (Norway began using the system on 1 November 2006). Denmark has begun running out of combinations in this style and has now introduced combinations previously reserved for Faroe Islands for EU style number plates (which will use different letters than non-EU style plates).
The Netherlands and Portugal both use three groups of two characters (letters or numbers) in several sequences: AB-12-CD, 12-34-AB, 12-AB-34, AB-12-34, etc. However, Portuguese plates have a white background, while those of Netherlands (after 1978-01-01) have a yellow one, though both countries also use white letters on blue plates for classic cars. Furthermore, newer plates on Dutch vehicles only contain consonants, to avoid coincidental abbreviations or words. Also some sensitive letter combinations, such as SS or SD, are not used. The combination 'AA' is reserved for cars of the royal family. Dutch company registered bus, truck and/or minivan plates always start with a B or a V. Dutch taxis use blue registration plates. The number of new combinations ran out in 2008. By now, new registered cars in the Netherlands use the following format of two digits-three letters-one digit (12-ABC-3).
Belgium used the sequence ABC-123 between 1973 and 2008. When these combinations ran out in 2008, the inverse sequence 123-ABC was adopted, with the first plate in the new series issued on June 25, 2008. With the introduction of the European format on November 15, 2010, a seven-character combination 1-ABC-234 is used and the previous 123-ABC was discontinued. However, the six-character plates will remain valid and no date is set for their expiration yet. Since Belgian plates are linked to an owner rather than to a vehicle, these older plates are likely to remain in use for a considerable time. As a way to phase out the six-character plates, future vehicle subscriptions will only be possible on the seven-character plates.
Luxembourg plates use two letters and four digits AB 1234. Older series with only three digits (AB 123) or all-numeric plates with up to five digits are no longer issued but are still in use.
Current registrations allocated in Romania and the United Kingdom (where the registration contains two digits) are both of the form AB12 CDE). The Romanian rear plates are white whereas UK ones are yellow. There is also a difference in the spacing and the font. In 2015, Bucharest, the capital of Romania, adopted the form B 123 AAA, three digits and three letters, because the number of cars had risen.
Sweden. Until 1973/74 the Swedish pattern was one letter representing the län (county) where the car was first registered, followed by four or five digits. However, in the more populated län, a second letter became introduced over time. F.i. vehicles from southernmost county got the letter M + five digits, later also MA + five digits, MB + five digits etc. A problem was that the two northernmost counties had already been given two letters, the letter prefixes AC and BD, as the number of usable letters exceeded the number of counties. The ABC 123 system was introduced gradually from July 1973 until June 1974.
Slovakia uses AB 123CD and Croatia uses AB 123-CD (in both cases also other patterns are possible). Both countries use a coat of arms after first two letters, and the fonts and colors also look very similar. The plates can be easily distinguished by country code on the blue strip on left.
Montenegro and Serbia, currently not members of the EU, used the following system until 2007: MM 12-34, MM 123-45 or MM 123-456 (MM being two letter abbreviation of municipality), and having state flag (of former Yugoslavia, later Serbia and Montenegro) between municipality and numbers. Montenegro left that system in 2007, and introduced new format: MM AB 123, with Montenegrin coat of arms in circular shape between municipality and letter sequence. Blue strip with MNE country code is placed in the left side, with vacant place for EU stars, in case of joining the Union. Serbia also uses new system with blue strip country code SRB: MM 123-AB and MM 1234-AB, with Serbian coat of arms between municipality and number sequence. The first two letters on the Serbian plates represent the municipality code, written in Latin letters, and repeated in Cyrillic characters with small letters under the coat of arms. The following system is used for taxi vehicles: BG 123 TX or BG 1234 TX and recently even BG 12345 TX, where a TX combination is reserved for this purpose only (another taxi vehicles have private vehicle plates). Since 2017, Serbia stopped issuing plates with last two letters containing W, Q, Y, X (except TX), Č, Ć, Š, Ž, and Đ, however Serbian Latin letters with diacritics are still used to mark the municipality code, like ČA for Čačak or ŠA for Šabac.
Differing numbering systems[edit]
Individual European countries use differing numbering schemes and text fonts:
Most countries, including Austria, Bulgaria, Croatia, the Czech Republic, Germany, Greece, Ireland, Macedonia, Montenegro, Norway, Poland, Romania, Serbia, Slovakia, Slovenia and Switzerland (formerly also Sweden-until 1974, Italy—until 1994, Bosnia and Herzegovina—until 1998, Lithuania and Spain —until 2000, Estonia -until 2004 and Albania —until 2011, of former countries also East Germany -until 1990, Soviet Union -until 1991, Czechoslovakia -until 1993, Yugoslavia -until 1998 and Serbia and Montenegro -until 2011), have systems in which there is a direct link between a letter or letters appearing on the plate and the town or district where the plate was issued (e.g. "B" and "M" in Germany for Berlin and Munich, "TN" and "ZV" in Slovakia for Trenčín and Zvolen, "BG" and "KG" in Serbia for Belgrade and Kragujevac and "AX" and "KY" in Greece for Achaea and Corfu). Some countries, including Austria, Germany, Slovenia, and Switzerland, even include a regional or municipal coat of arms on the plate, but Croatia, Montenegro, Serbia and Slovakia includes a national coat of arms. In Ireland, all plates have the name of the county of registration in Irish in smaller letters on the top.
France (until 2009), Turkey and Russia (since October 2013) use a system with an indirect number relation to the car's place of registration.
The UK uses a system based on the region where the car was first registered and the date of registration, for example CA52 GJK, where by the "C" stands for Wales (the name of that country in Welsh being Cymru), the "A" stands for Cardiff (the letters A-O assigned to the city), and the "52" means that the car was registered in the year 2002, in or after September.
Belgium, Bosnia and Herzegovina, Denmark, Iceland, Estonia (after 2004), Finland, Hungary, Latvia, Lithuania (after 2000), Luxembourg, the Netherlands, Portugal and Sweden (after 1974) use plates that do not denote location where the car is registered. Since 2000 Spain no longer uses province codes on plates but codes like 'B' for Barcelona or 'M' for Madrid can still be seen, for cars registered before that date. Italy, also, doesn't have used the province codes on plates between 1994 and 1999.
Italy, since 1999, has added a blue strip on either side. On the right one are the two digits of the year when the plate was issued (e.g. "99", "05", "08") and below that there may be an optional two-letter code for the province, such as "MO" for the Province of Modena. Albania and France have adopted similar formats.
Irish license plates also contain the year in which the vehicle was registered. A car registered in 2008 would have the format 08-XX-XXXX. In 2013, this was updated to specify which half of the year the registration occurred. So from January to June, the license plate would show (for 2013) 131-XX-XXXX, whereas from June to December, the plate instead shows 132-XX-XXXX.
Cross-border traffic[edit]
Vehicles in cross-border traffic are obliged to display a distinguishing sign of the country of registration on the rear of the vehicle. This sign may either be placed separately from the registration plate or may be incorporated into the vehicle registration plate (such as the EU strip).
The physical requirements for the separate sign are defined in Annex 3 of the Vienna Convention on Road Traffic, which states that the letters shall be in black on a white background having the shape of an ellipse with the major axis horizontal. The distinguishing sign should not be affixed in such a way that it could be confused with the registration number or impair its legibility.
When the distinguishing sign is incorporated into the registration plate, it must also appear on the front registration plate of the vehicle, and may be supplemented with the flag or emblem of the national state, or the emblem of the regional economic integration organization to which the country belongs. The distinguishing sign should be displayed on the far left or far right on the registration plate. When a symbol/flag/emblem is also displayed, the distinguishing sign shall obligatory be placed on the far left on the plate. The distinguishing sign shall be positioned so to be easy identifiable and so that it cannot be confused with the registration number or impair its legibility. The distinguishing sign shall therefore be at least a different color from the registration number, or have a different background color to that reserved for the registration number, or be clearly separated from the registration number, preferably with a line.[7]
Vehicles with EU number plates do not need to display the white oval international vehicle registration code while within the European Economic Area. Because of the way in which the Council Regulation implementing the EU Symbol (Regulation No. 2411/98) is drafted, the EU format is optional in Denmark, Finland, the United Kingdom and Cyprus. The regulation only requires states that have ratified the Vienna Convention of 1968 on road traffic to enforce the EU symbol. This can be seen in Article 3, which reads: "Member States requiring vehicles registered in another Member State to display a distinguishing registration sign when they are being driven on their territory shall recognise the distinguishing [EU Symbol] sign"
The 'requirement', "to display a distinguishing registration sign" is derived directly from Article 37 of the 1968 Vienna Convention on Road Traffic (this is actually stated in preamble (3) of Regulation 2411/98). So in order for Reg 2411/98 to apply, the state must have ratified the 1968 Convention. Since Denmark, Finland and the UK have not ratified it, Regulation 2411/98 technically does not apply and therefore the EU symbol is not a mandatory requirement in those states.
Countries[edit]
Dependencies, partially recognized and disputed territories[edit]
List[edit]
Vehicle registration plates of each country are described in the following table:
Countries [8][edit]
Country
Code
Example
Albania AL
Andorra AND
Armenia AM
Austria A
Azerbaijan AZ
Belarus BY
Belgium B
Bosnia and Herzegovina BIH
Bulgaria BG
Croatia HR
Cyprus CY
Czech Republic CZ
Denmark DK
Estonia EST
Finland FIN
France F
Georgia GE
Germany D
Greece GR
Hungary H
Iceland IS
Ireland IRL
Italy I
Latvia LV
Liechtenstein FL
Lithuania LT
Luxembourg L
Macedonia MK
Malta M
Moldova MD
Monaco MC
Montenegro MNE
Netherlands NL
Norway N
Poland PL
Portugal P
Romania RO
Russia RUS
San Marino RSM
Serbia SRB
Slovakia SK
Slovenia SLO
Spain E
Sweden S
Switzerland CH
Turkey TR
Ukraine UA
United Kingdom GB
Vatican City V
Dependencies, partially recognized and disputed territories[edit]
Territory
Code
Example
Abkhazia ABH
Åland Islands AX
Gibraltar GBZ
Faroe Islands FO
Guernsey GBG
Isle of Man GBM
Jersey GBJ
Kosovo[a] RKS
Northern Cyprus CY
South Ossetia RSO
Transnistria PMR
Motorcycle plates[edit]
These are used for motorcycles and vehicles where mounting space is an issue, such as taxis which display their licence plate beside the registration plate, and vehicles imported from countries where the mounting space was not originally designed to take European-sized plates (e.g. USA).
Countries[edit]
Country
Code
Example
Belarus BY
France F
Germany D
Italy I
Latvia LV
Macedonia MK
Malta M
Moldova MD
Monaco MC
Montenegro MD
Norway N
Poland PL
Serbia SRB
Spain E
Sweden S
Turkey TR
Ukraine UA
United Kingdom
GB
Dependencies, partially recognized and disputed territories[edit]
Territory
Code
Example
Kosovo[a] RKS
South Ossetia RSO
Transnistria PMR
See also[edit]
List of international vehicle registration codes
Vehicle registration plates of the European Union
Notes and references[edit]
Notes:
a. ^ Kosovo is the subject of a territorial dispute between the Republic of Kosovo and the Republic of Serbia. The Republic of Kosovo unilaterally declared independence on 17 February 2008, but Serbia continues to claim it as part of its own sovereign territory. The two governments began to normalise relations in 2013, as part of the Brussels Agreement. Kosovo has received formal recognition as an independent state from 112 out of 193 United Nations member states.
References:
Jump up ^ http://www.international-driving-permit.com/Convention-on-Road-Traffic/8-November-1968/EN/Annexex/Annex-3-Distinguishing-Sign-of-Motor-Vehicles-and-Trailers-to-International-Traffic.aspx
Jump up ^ "EUR-Lex - 31998R2411 - EN - EUR-Lex". Retrieved 26 May 2016.
Jump up ^ "S.I. No. 287/1990 - Road Vehicles (Registration and Licensing) (Amendment) Regulations, 1990". Retrieved 26 May 2016.
Jump up ^ "License Plates of". Retrieved 26 May 2016.
Jump up ^ "License Plates of Germany". Retrieved 26 May 2016.
Jump up ^ "Indførelse af danske EU nummerplader i oktober 2009" (in Danish).
Jump up ^ http://www.international-driving-permit.com/Convention-on-Road-Traffic/8-November-1968/EN/Annexex/Annex-3-Distinguishing-Sign-of-Motor-Vehicles-and-Trailers-to-International-Traffic.aspx
Jump up ^ http://matriculasdelmundo.com/europeas.php European license plates
External links[edit]
Media related to License plates of Europe at Wikimedia Commons
[hide]
v
t
e
Vehicle registration plates of Europe
Sovereign states
Albania
Andorra
Armenia
Austria
Azerbaijan
Belarus
Belgium
Bosnia and Herzegovina
Bulgaria
Croatia
Cyprus
Czech Republic
Denmark
Estonia
Finland
France
Georgia
Germany
Greece
Hungary
Iceland
Ireland
Italy
Kazakhstan
Latvia
Liechtenstein
Lithuania
Luxembourg
Macedonia
Malta
Moldova
Monaco
Montenegro
Netherlands
Norway
Poland
Portugal
Romania
Russia
San Marino
Serbia
Slovakia
Slovenia
Spain
Sweden
Switzerland
Turkey
Ukraine
United Kingdom
Vatican City
States with limited
recognition
Abkhazia
Artsakh
Kosovo
Northern Cyprus
South Ossetia
Transnistria
Dependencies and
other entities
Åland
Faroe Islands
Gibraltar
Guernsey
Isle of Man
Jersey
Svalbard
Other entities
European Union
Sovereign Military Order of Malta
Retrieved from "https://en.wikipedia.org/w/index.php?title=Vehicle_registration_plates_of_Europe&oldid=815099304"
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Cluster B personality disorders
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Personality disorders
Cluster A (odd)
Paranoid
Schizoid
Schizotypal
Cluster B (dramatic)
Antisocial
Borderline
Histrionic
Narcissistic
Cluster C (anxious)
Avoidant
Dependent
Obsessive–compulsive
Not specified
Depressive
Haltlose
Passive–aggressive
Sadistic
Self-defeating
Psychopathic
v
t
e
Cluster B personality disorders are a categorization of personality disorders as defined in the DSM-IV and DSM-5.[1]
Cluster B personality disorders are characterized by dramatic, overly emotional or unpredictable thinking or behavior and manipulative, exploitative interactions with others. They include antisocial personality disorder, borderline personality disorder, histrionic personality disorder and narcissistic personality disorder.[2]
The British National Health Service has described those with this disorder as someone who, "struggles to relate to others. As a result, they show patterns of behaviour most would regard as dramatic, erratic and threatening or disturbing."[3]
There are four recognized Cluster B personality disorders:[4]
Antisocial personality disorder (DSM-IV code 301.7): a pervasive disregard for the law and the rights of others.
Borderline personality disorder (DSM-IV code 301.83): extreme "black and white" thinking, instability in relationships, self-image, identity and behavior often leading to self-harm and impulsivity.
Histrionic personality disorder (DSM-IV code 301.50): pervasive attention-seeking behavior including inappropriately seductive behavior and shallow or exaggerated emotions.
Narcissistic personality disorder (DSM-IV code 301.81): a pervasive pattern of grandiosity, need for admiration, and a lack of empathy.
See also[edit]
Personality disorders in the DSM-5
References[edit]
Jump up ^ Kristalyn Salters-Pedneault (May 6, 2016). "Understanding the Cluster B Personality Disorders/The Cluster B Personality Disorders: What Are the Cluster B Personality Disorders?". Verywell. Archived from the original on September 6, 2010.
Jump up ^ http://www.mayoclinic.org/diseases-conditions/personality-disorders/symptoms-causes/dxc-20247656
Jump up ^ http://www.nhs.uk/conditions/personality-disorder/Pages/Symptoms.aspx
Jump up ^ http://www.mayoclinic.org/diseases-conditions/personality-disorders/symptoms-causes/dxc-20247656
[1]
Jump up ^ https://counsellingresource.com/therapy/self-help/understanding/
Retrieved from "https://en.wikipedia.org/w/index.php?title=Cluster_B_personality_disorders&oldid=819238033"
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