# Sound energy

Sound quantities

The sound energy  W is the energy contained in a sound field or a sound event . The unit of measurement for sound energy is the Joule  J. The corresponding logarithmic quantity is the sound energy level .

## definition

Sound vibrations and sound waves go hand in hand with small alternating movements of particles in the medium in which the sound is propagating. That is why sound waves possess and transport kinetic energy . At the same time there is an alternating compression and dilution of parts of this medium. This absorbs and releases potential energy .

The sound energy of a sound field can be calculated as the sum of kinetic and potential energy. In the case of sound propagation in a fluid, the following applies:

{\ displaystyle {\ begin {aligned} W & = W _ {\ mathrm {pot}} && + W _ {\ mathrm {kin}} \\ & = \ int _ {V} {\ frac {p ^ {2}} { 2 \ rho _ {0} c ^ {2}}} \, \ mathrm {d} V && + \ int _ {V} {\ frac {\ rho v ^ {2}} {2}} \, \ mathrm { d} V \ end {aligned}}}

Are there

• ${\ displaystyle p}$the sound pressure
• ${\ displaystyle \ rho _ {0}}$the density
• ${\ displaystyle c}$the speed of sound in the fluid
• ${\ displaystyle v}$the speed of sound
• ${\ displaystyle V}$the volume .

${\ displaystyle W = I \; t \; A}$

With

• the sound intensity ${\ displaystyle I}$
• currently ${\ displaystyle t}$
• the area through which the air flows .${\ displaystyle A}$

It often makes sense to consider the sound energy density as a variable that depends on the location instead of the sound energy . For the calculation it is not necessary to integrate over the volume of the sound field: ${\ displaystyle E ({\ vec {x}})}$${\ displaystyle {\ vec {x}}}$

${\ displaystyle E ({\ vec {x}}) = {\ frac {\ mathrm {d} W} {\ mathrm {d} V}} \ Leftrightarrow W = \ int _ {V} E ({\ vec { x}}) \, \ mathrm {d} V}$

The rate of sound energy emitted by a sound source is the sound power of that source: ${\ displaystyle P _ {\ mathrm {ak}}}$

${\ displaystyle {\ frac {\ mathrm {d} W} {\ mathrm {d} t}} = P _ {\ mathrm {ak}}}$

The acoustic energy (or sound energy level) is also used for detecting a pulse -like sound operation and is determined by integrating the noise power over the whole process, including the pulse decay time obtained:

${\ displaystyle \ Leftrightarrow W = \ int _ {t} P _ {\ mathrm {ak}} \, \ mathrm {d} t}$

In the case of point sources, the sound energy quantities decrease by 1 / r 2 over the distance r ( distance law ).

## Sound energy level

It is also common to state the sound energy as the sound energy level  L I in decibels  (dB):

${\ displaystyle L_ {W} = 10 \ lg \ left ({\ frac {W} {W_ {0}}} \ right) \, \ mathrm {dB}}$

with the standardized reference value (acoustics) W 0 = 10 −12  J.