# 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 ${\ displaystyle v}$ 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