Speed of sound

acoustic measurements
sound pressure p
sound pressure level L p
acoustic velocity v
acoustic velocity level L v
sound deflection ξ
sound acceleration A
loudness I
loudness level L I
sound power P AC
sound-power level L W
Schallenergiedichte E
Schallfluss q
acoustical impedance Z
sound radiation impedance Z 0
speed of sound C

the speed of sound C is the speed, with which acoustic waves in any medium (usually in air) spread. It is the propagation speed of the audible sound, which is not to be confounded v with the acoustic velocity. SI - Unit of the speed of sound is meter per second (m/s).
For the speed of sound C (for lat. celeritas = speed) the formula applies

< math>

C = \ lambda \ f cdot </math>,

whereby λ (lambda) the wavelength and f are the frequency of the acoustic wave.

Table of contents

speed of sound in solids

acoustic waves in solids being able bothin more longitudinal (here is parallel the oscillation direction to the direction of propagation) and in transverse direction (here the oscillation direction is perpendicular to the direction of propagation) spread.

For longitudinal waves generally case hangs the speed of sound in solids of the density <math> \ rho< /math>, the Poissonzahl< math> \ mu< /math> andthe modulus of elasticity E of the solid body off. It applies thereby

< math>

c_ {\ mathrm {Festk \ ddot more orper, longitudinal}} = \ sqrt {E \, (1 - \ mu) \ more over \ rho \, (1 - \ mu - 2 \ mu^2)} </math>.

In the special case of a long staff, whereby the diameter of the staffthan the wavelength of the acoustic wave to be clearly smaller, can the lateral contraction must be neglected and one receives

< math>

c_ {\ mathrm {Festk \ ddot orper (long staff), longitudinal}} = \ sqrt {E \ over \ rho} </math>.

For transverse waves that must modulus of elasticity by shear modulus <math> the G< /math> are replaced

< math>

c_ {\ mathrm {Festk \ ddot more orper, transverse}} = \ sqrt {G \ more over \ rho} </math>.

only longitudinal waves

can spread speed of sound in liquids contrary to solids in liquids, since that is alike to shear modulus for liquids zero. The speed of sound is a function of the density<math> \ rho< /math> and the bulk modulus <math> K< /math> the liquid and computes itself out

< math>

c_ {\ mathrm {flat steel bar \ ddot ussigkeit}} = \ sqrt {K \ more over \ rho} </math>. This applies only in the static condition of a liquid. If this should move, then it comes to run time differences.

The effects of theseEquation can be demonstrated with the Cappuccino effect. If one agitates up-foamed milk in coffee and knocks then with the spoon several times in short distances on the soil of the cup, the sound changes. With the Unterrühren of the milk foam the knocking noises becomefirst more deeply and afterwards more highly, since with and then slowly escaping air included first in the foam the bulk modulus of the coffee changes.

speed of sound in ideal gases

the speed of sound in ideal gases depends on the adiabatic curve exponent κ (kappa), the density ρ (rho) as well as the pressure p of the gas or alternatively after the thermal equation of state of the molecular mass M and the absolute temperature T (measured in Kelvin) and computes itself out

< math>

c_ {\ mathrm {gas}} = \ sqrt {\ kappa \ cdot{p \ more over \ rho}} = \ sqrt {\ kappa \ cdot \ frac {R \ cdot T} {M}} </math>. whereby M = 0.02896 is kg/mol the molecular mass and κ = 1.402 the adiabatic curve exponent of air. The adiabatic curve exponent κ (kappa) = C p/C V hangs also formost material gases over far temperature ranges from T , the molecular mass is not a material-specific and the universal gas constant of R = 8.3145 J/molK a physical constant. A more exact empirical expression for the speed of sound arises as a result of summarizingthe constants into a only one computational constant:

<math>

c_ {\ mathrm {air}} \ approx \ sqrt {1 {,} 402 \ cdot \ frac {R \ cdot T} {0 {,} 02896 \, \ mathrm {kg/mol}}} = 20 {,} 055 \ sqrt {T \ more over \ mathrm {K}} \ \ mathrm {m/s} </math>

Therefore the speed of sound in ideal gases depends only on the root (absolute) of the temperature.


Despite the root dependingness the linear becomes frequentNäherungsformel

< math>

c_ {\ mathrm {air}} \ approx (331 {,} 5 + 0 {,} 6 \ cdot \ vartheta) \ \ mathrm {m/s} </math>

used, whereby <math> \ vartheta=T-273 {,} 15 \, \ mathrm {K}< /math> the temperature in °C is.


The exact amount of the Vorfaktoren became from measurements after D.A. Bohn (1988) determines. With this equation the speed of sound amounts to25 °C (= 298.15 K) about 346 m/s. More generally is the value C = 343 admits m/s for 20 °C (room temperature).

This Näherungsformel applies in the temperature range from -20°C to +40°C with an accuracy of better than 0.2%. ThoseSpeed of sound is independent of the air pressure. The air humidity affected slightly the speed of sound and also the often incorrectly indicated static sound pressure does not do it (exceptions are acoustic waves of very large amplitude as well as shock waves). Against it the temperature is very important. ThatSound moves within the troposphere more slowly with rising height, which however almost exclusively a function of the temperature is and only in small measure also one the humidity.

Comparisons for this the standard conditions and the standard conditions. Normally the speed of sound becomes under Standard atmosphere measured.

With an ideal gas the speed of sound depends and independent only on the temperature on the air pressure. This dependence therefore applies also to air which can be regarded in good approximation as ideal gas.

examples ofSound speeds in different media

in the following table are listed some examples of sound speeds in different media at a temperature of 20 °C. Left: Pressure wave (longitudinal). Right: Speed of sound after Wellenumwandlung (transverse), this wave develops in a firm subsequent medium with Schrägeinschallungand spreads perpendicularly to the actual pressure wave.

Medium speed of sound
in (m/s)
transverse
in (m/s)
air (with 20 °C) 343 (*)  
Helium 981  
Hydrogen 1280  
Oxygen 316  
Water 1484  
Water (with 0 °C) 1407  
Ice (with -4 °C) 3250  
Oil (SOW 20/30) 1740  
Glass of 5300  
PVC (soft) 80  
PVC (hard) 2250 1060
concrete 3100  
Beech wood 3300  
Aluminum 6300 3080
beryllium 12900 8880
lead /5 %Antimon 2160 700
gold 3240 1280
copper 4660 2260
magnesium /Zk60 4400 810
mercury 1450  
Steel 5920 3255
titanium 6100 3050
tungsten 5460 5460
iron 5170  

(*) 1234.8 km/h correspond.

In beryllium the sound achieves the highest calculated speed of sound.

temperature dependence

Generally the following dependence on the temperature results math \ vartheta_ <{>0} [K] /math for< the speed of sound>.

<math> c=c_ 0 \ sqrt {{\ frac {\ vartheta} {\ vartheta_ 0}}}< /math>

C 0 [ in m/s] places the speed with <math> \ vartheta_ {0} = 273 K< /math> and C [in m/s] the Schallgewindigkeit<math> \ vartheta [K]< /math>.

The temperature dependence arises as a result of very large density gradients and changes of speed in the case of the produced waves. Because thus are no longer fulfilled the approximations to hydrodynamic Basic Law width units.


Thus the for example following table for air with C 0 = 331.5 m/s results.Here the air pressure does not have effect on the speed of sound, even if this false indication is to be found frequent.


Sound radiation impedance, atmospheric pressure and speed of sound as a function of the air temperature
temperature
< math> \ vartheta< /math> in °C
speed of sound
C in m/s
density
ρ in kg/m 3
knowing impedance
Z F in Ns/m 3
,-10 325.4 1.341 436.5
-5 328.5 1.316 432.4
0 331.5 1.293 428.3
5 334.5 1.269 424.5
10 337.5 1.247 420.7
15 340.5 1.225 417.0
20 343.4 1.204 413.5
25 346.3 1.184 410.0
30 349.2 1,164 406,6

frequency response

in a dispersiven medium the speed of sound depends on the frequency. The spatial and temporal distribution of a reproduction disturbance constantly changes. Each frequency component reproduces itself in each case with its own phase velocity, while the energy thatDisturbance with the group velocity reproduces itself. Water is an example of a dispersiven medium.

In a dispersiven medium the speed of sound is independent of the frequency. Therefore the speeds of the energy transfer and sound propagation are the same. Air is a not dispersivesMedium.

other

in aviation is measured the speed of an airplane also relative to the speed of sound. The unit Mach is used, whereby 1 Mach is equal to the respective speed of sound. See also: Supersonic speed, supersonic flight.

The distancea thunderstorm can be measured, by counting the seconds after seeing lightning up to hearing the thunder. The number of seconds divided by three results in about the distance of the thunderstorm in kilometers.

See also

Wiktionary: Speed of sound - word origin, synonyms and translations

literature

  • Dennis A. Bohn, Environmental Effects on the speed OF sound, journal OF the audio engineering Society, 36 (4), April 1988. Pdf version

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