sound energy density
{{distinguish|Sound pressure}}
{{Sound measurements}}
Sound energy density or sound density is the sound energy per unit volume. The SI unit of sound energy density is the pascal (Pa), which is 1 kg⋅m−1⋅s−2 in SI base units or 1 joule per cubic metre (J/m3).{{cite report | editor-last=Newell | editor-first=David B | editor-last2=Tiesinga | editor-first2=Eite | title=The international system of units (SI) | publisher=National Institute of Standards and Technology | publication-place=Gaithersburg, MD | year=2019 | doi=10.6028/nist.sp.330-2019 | url = https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.330-2019.pdf}}{{rp|at= Section 2.3.4: Derived units, Table 4}}
Mathematical definition
Sound energy density, denoted w, is defined by
:
where
- p is the sound pressure;
- v is the particle velocity in the direction of propagation;
- c is the speed of sound.
The terms instantaneous energy density, maximum energy density, and peak energy density have meanings analogous to the related terms used for sound pressure. In speaking of average energy density, it is necessary to distinguish between the space average (at a given instant) and the time average (at a given point).
Sound energy density level<!--'Sound energy density level' redirects here-->
The sound energy density level gives the ratio of a sound incidence as a sound energy value in comparison to the reference level of 1 pPa (= 10−12 pascals).Deutsches Institut für Normung, Grundlagen der Schallmessung; Physikalische & subjektive Größen von Schall, Physical & subjective magnitudes of sound, Norm, Standard, № [https://dx.doi.org/10.31030/1234608 DIN 45630‑1:1971‑12] (Berlin: Beuth, 1971‑12). It is a logarithmic measure of the ratio of two sound energy densities. The unit of the sound energy density level is the decibel (dB), a non-SI unit accepted for use with the SI Units.{{rp|at=| Chapter 4: Non-SI units that are accepted for use with the SI, Table 8}}
The sound energy density level, L(E), for a given sound energy density, E1, in pascals, is
:
L(E) = 10\, \log_{10}\left(\frac{E_1}{E_0}\right) ~ \text{dB}
,
where E0 is the standard reference sound energy densityDeutsches Institut für Normung, Akustik—Begriffe, Acoustics—Terminology, Norm, Standard, № [https://dx.doi.org/10.31030/1544140 DIN 1320:2009-12] (Berlin: Beuth, 2009‑12).
:
E_0 = 10^{-12}\ \mathrm{Pa}
.
See also
References
External links
- [http://www.sengpielaudio.com/calculator-soundlevel.htm Conversion: sound intensity to sound intensity level]
- [http://www.sengpielaudio.com/calculator-ak-ohm.htm Ohm's law as acoustic equivalent - calculations]
- [http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf]