# What is the integral of the sound intensity

The sound power emitted by sound sources cannot be recorded directly, but requires the measurement of other variables that describe the sound field, e.g. the sound pressure and the room acoustics, in order to then calculate the sound power. The following procedures can be distinguished:

Enveloping surface method (sound pressure and sound intensity method)

Reverberation room method

Comparative sound source method

These procedures are briefly outlined here. The details of the implementation of corresponding noise emission measurements according to the enveloping surface method, for example for determining the measuring points, determining room influence and background noise correction, as well as the different measurement standards are described in detail in the pocket book "Noise Measurement in Operation".

**1****Enveloping surface method**

Of the various methods for determining the sound power level, the enveloping surface method has become the most popular in operational practice, as it can be carried out directly at the installation site of the machines if the spatial conditions and the effects of extraneous noise meet certain requirements.

At the **Enveloping surface method**the sound power emitted by a noise source through**Measurement at numerous measuring points**on one including the source**imaginary enveloping surface / measuring surface S**recorded (see**Image 1**). When the machine is usually set up on a reflective floor, this envelope surface is either hemispherical or cuboid and ends on the floor.

To record the sound energy penetrating this area, sound pressure level measurements in accordance with DIN EN ISO 3744 to 3746 or sound intensity measurements in accordance with DIN EN ISO 9614-1, -2 and -3 can be carried out.

The enveloping surface method is based on the approach of determining the sound power P of a sound source by integrating the sound intensity I over a measuring surface S that completely surrounds the source (see **Image 1**):

P = (1)

with I._{n}= I.cos- Normal component of the sound intensity on the measuring surface.

**Image 1:**Acquisition of the sound power on a hemispherical measuring surface

In measuring practice, the integral described in equation 1 is approximated by dividing the measuring area S into n partial measuring areas S._{i}decomposed and for this the sound intensities I_{ni}detected. The sound power then results from the following formula:

* P.*=(2)

With*I. _{ni}*-Sound intensity of the partial measuring area

*S.*

_{i}*S. _{i}*-i-th partial measuring area

This sound power corresponds to the product of the sound intensity averaged over the measurement area*I. _{n}*and the measuring surface

*S.*:

* P.*=`*I. _{n}*

*S.*(3)

with`*I. _{n}*- Average sound intensity flowing through the measuring surface S perpendicularly

*S.*-Measuring area.

The mean sound intensity '*I. _{n}*is determined in measuring practice by placing a sufficiently large number of measuring points evenly over the cuboid or hemispherical measuring surface

*S.*distributed, the sound intensity is recorded perpendicular to the surface and the measured values are energetically averaged. More detailed information on the arrangement of the measuring points can be found in the corresponding measuring standards.

The sound power level L_{W.}then results with reference to the specified reference sound power P_{0}according to the following equation:

L._{W.}= 10lgdB (4)

L._{W.}= 10lgdB (5)

With:

P._{0}=110^{-12}W (= I_{0}S._{0}) - reference sound power

I._{0}=110^{-12}W / m^{2}- reference intensity (hearing threshold)

S._{0}= 1m^{2}- reference area

Equation (5) can be converted into the following sum formula:

L._{W.}= 10 lgdB (6)

The first summand 10 lg (/ I_{0}) corresponds to the mean sound intensity level L._{I.}on the measuring surface. Since the sound intensity level L_{I.}in a plane sound wave (ideal free field conditions) with the sound pressure level L._{p}matches (see e.g. Maue "0 decibels + 0 decibels = 3 decibels"), the sound power level L_{W.}under these conditions also calculate using the mean sound pressure level.

The sound power level L |

L. or in the plane sound wave (free field + far field): L. |

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