Sound energy density

Sound quantities

Sound deflection ${\displaystyle \xi }$ Sound pressure ${\displaystyle p}$ Sound pressure level ${\displaystyle L_{p}}$ Sound energy density ${\displaystyle E}$ Sound energy ${\displaystyle W}$ Sound flow ${\displaystyle q}$ Speed ​​of sound ${\displaystyle c_{\text{S}}}$ Acoustic impedance ${\displaystyle Z}$ Sound intensity ${\displaystyle I}$ Sound power ${\displaystyle P_{\text{ak}}}$ Speed ​​of sound ${\displaystyle v}$ Fast sound amplitude ${\displaystyle v}$ Sound radiation pressure

The sound energy density (symbol E or w ) is a measure to describe the sound energy present at a certain location in the sound field . It is a sound energy quantity . The associated logarithmic quantity is the sound energy density level.

definition

The sound energy density  E is the sound energy per volume unit:

${\displaystyle E={\frac {dW({\vec {x}})}{dV}}}$

It gives information about the sound energy  W at a certain location of a sound field and is its energy density . ${\displaystyle {\vec {x}}}$

The unit of sound energy density is joules per cubic meter  (J / m³).

In the special case of the even advancing wave, the time-averaged sound energy density is:

${\displaystyle {\bar {E}}={\frac {I}{c}}}$,

where I is the sound intensity and c is the speed of sound .

Sound energy density level

Occasionally the sound energy density is also given in the form of a sound energy density level L _E in decibels  (dB):

${\displaystyle L_{E}=10\,\log _{10}\left({\frac {E_{1}}{E_{0}}}\right){\rm {dB}}.}$

The reference value is defined as J / m³ or W · s / m³. ${\displaystyle E_{0}=10^{-12}}$

Relationships in the plane wave

Further formulas for the sound energy density for flat, progressing sound waves:

${\displaystyle E=\xi ^{2}\cdot \omega ^{2}\cdot \rho =v^{2}\cdot \rho ={\frac {a^{2}\cdot \rho }{\omega ^{2}}}={\frac {p^{2}}{Z\cdot c}}={\frac {I}{c}}={\frac {P_{ak}}{c\cdot A}}}$

Where:

symbol	units	meaning
E.	W · s / m 3	Sound energy density
ξ	m , meter	Sound deflection
${\displaystyle \omega }$= 2 · · f ${\displaystyle \pi }$	rad / s	Angular frequency
ρ	kg / m 3	Air density , density of the air (of the medium)
v	m / s	Speed ​​of sound
a	m / s 2	Sound acceleration
p	Pascal	Sound pressure
f	hertz	frequency
Z = c ρ	N · s / m 3	Characteristic acoustic impedance, acoustic field impedance
I.	W / m 2	Sound intensity
c	m / s	Speed ​​of sound
P ak	W, watt	Sound power
A.	m 2	Transmitted surface

Web links

• Sound energy density and the relationship between the acoustic quantities in the case of flat, progressing sound waves (PDF; 109 kB)
• Sound quantities, their levels and the reference value - conversions, calculations and formulas

Individual evidence

1. ↑ DIN 1320: Acoustics: Terms . Edition 1997-06.