Speed of sound
Those Speed of sound C is those Speed, with that itself Acoustic waves spread in any medium (usually in air). It is the propagation rate, not with that Acoustic velocity v to confound is. Those SIUnit of the speed of sound is Meter per Second (ms).
For the speed of sound C (lat for. celeritas = speed) the formula applies
- <math>
C = \lambda \cdot f </math>,
how? (lambda) those Wavelength and f those Frequency the acoustic wave is.
Table of contents |
Speed of sound in solids
Acoustic waves in Solids can itself both in more longitudinal (here the oscillation direction is parallel 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 that Density <math> \rho</math>, that Poissonzahl <math> \mu</math> and that Modulus of elasticity E 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 staff must be clearly smaller than the wavelength of the acoustic wave, the lateral contraction can be neglected and one receives
- <math>
c_{\mathrm{Festk \ddot orper (long staff), longitudinal}} = \sqrt{E \more over \rho} </math>.
For transverse waves that must modulus of elasticity by that Shear modulus <math>G</math> are replaced
- <math>
c_{\mathrm{Festk \ddot more orper, transverse}} = \sqrt{G \more over \rho} </math>.
Speed of sound in liquids
Contrary to solids can itself in Liquids only longitudinal waves spread, since that is alike to shear modulus for liquids zero. The speed of sound is < a function of the density;math> \rho</math> and of the Bulk modulus <math>K</math> the liquid and computes itself out
- <math>
c_{\mathrm{Fl \ddot ussigkeit}} = \sqrt{K \more over \rho} </math>. This applies only in the static condition of a liquid. This should move, thus it comes to run time differences.
The effects of this equation can with that Cappuccino effect are demonstrated. One agitates up-foamed milk in coffee and knocks then with the spoon several times in short distances on the soil of the cup, changes the sound. With the Unterruehren of the milk foam the knocking noises become first deeper and afterwards higher, 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 Adiabatic curve exponent ? (kappa), that Density ? (rho) as well as that Pressure p the gas or alternatively after that thermal equation of state of that molecular measures M and the absolute Temperature T (measured in Kelvin) computes itself and out
- <math>
c_{\mathrm{Gas}} = \sqrt{\kappa \cdot {p \more over \rho}} = \sqrt{\kappa \cdot \frac{R \cdot T}{M}} </math>.
That Adiabatic curve exponent ? (kappa) = Cp/CV hangs also for most material gases over far temperature ranges not of T off, the molecular mass is a material-specific and a those universal gas constant R = 8.3145 jone milked physical constant.
Therefore the speed of sound in ideal gases depends only on the root (absolute) of the temperature. Despite the root dependingness the linear naeherungsformel becomes frequent
- <math>
c_{\mathrm{Luft}} \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. This naeherungsformel applies in the temperature range from -20°C to +40°C with an accuracy of better than 0,2%. The speed of sound is independent of Air pressure. Those Air humidity affected slightly the speed of sound and also the often incorrectly indicated static Sound pressure it does not do (exceptions are acoustic waves of very large amplitude as well as Shock waves). Against it the temperature is very important. The sound moves within that 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.
A more exact empirical expression for the speed of sound arises as a result of summarizing the constants into a only one computational constant:
- <math>
c_{\mathrm{Luft}} \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>
how M = 0.02896 kgmol the molecular mass and ? = 1.402 the adiabatic curve exponent of air is. The exact amount of the Vorfaktoren became from measurements after D.A. Bohn (1988) determines. With this equation the speed of sound amounts to with 25 °C (= 298.15 K) about 346 ms. More generally is the value admits C = 343 ms for 20 °C (Room temperature).
Comparisons for this those Standard conditions and those Standard conditions.
Normally the speed of sound becomes with that Standard atmosphere measured.
With an ideal gas the speed of sound depends and independent only on the temperature on the air pressure. This dependence applies therefore also to air, in good approximation as ideal gas to be regarded can.
Examples of sound speeds in different media
In the following table some examples of sound speeds in different media are at a temperature of 20 °C listed. Left: Pressure wave (longitudinal). Right: Speed of sound after wellenumwandlung (transverse), this wave develops in a firm subsequent medium with Schraegeinschallung and spreads perpendicularly to the actual pressure wave.
| Medium | Speed of sound in (ms) | Transverse in (ms) |
|---|---|---|
| Air (with 20 °C) | 343 (*) | |
| Helium | 981 | |
| Hydrogen | 1280 | |
| Oxygen | 316 | |
| Water | 1484 | |
| Water (with 0 °C) | 1407 | |
| Ice (with -4 °C) | 3250 | |
| Oil(SAE 20/30) | 1740 | |
| Glass | 5300 | |
| PVC (softly) | 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 |
(*) 1234.8 km correspondh. In Beryllium achieves the sound the highest calculated speed of sound.
Temperaturabhd.ngigkeit
Würfel starke Wirkung der Lufttemperatur &.lt;math>T</math> on the speed of sound <math>c</math> is represented in the following table. Z.B. is C = 343 ms with 20 °C. Here that has Air pressure no effect on the speed of sound, even if this false indication is to be found frequent.
| Temperature T in °C | Speed of sound C in ms | Density ? in kgm3 | Knowing impedance ZF in LVm3 |
|---|---|---|---|
| -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 one dispersiven Medium is the speed of sound of that Frequency dependently. 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 of the disturbance reproduces itself with the group velocity. 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 dispersives medium.
Other
In aviation the speed of an airplane is measured also relative to the speed of sound. The unit becomes Mach used, how 1 Mach equal to the respective speed of sound is. See also: Supersonic speed, Supersonic flight.
The distance one Thunderstorm can be measured, by one after seeing of the Lightning the seconds counts up to hearing of the Thunder. The number of seconds divided by three results in about the distance of lightning in kilometers.
See also
| - word origin, Synonymous one and translations |
- Speed of light
Literature
- Dennis A. Bohn, Environmental Effects on the speed OF sound, Journal OF the audio engineering Society, 36(4), April 1988. Pdf version
Web on the left of
- Computation of the speed of sound in air
- The speed of sound, the temperature and... not the air pressure
- Computation of wavelength, Frequency and speed of sound or speed of light
- Computation of the wavelength of an acoustic wave in air at given frequency and temperature
- Measurement of the speed of sound in metals
- Good sound bases
