# Substitution method for sound power determination

28.11.2019

The sound emission of technical devices, machinery and equipment has to be declared for purposes of environmental protection, occupational health and consumer information. An upper limit for the sound emission is legally binding for some machines used outdoors. The descriptor for sound emission is the sound power level, which is measured by internationally harmonised methods. A disadvantage of today’s methods is that sound at frequencies below about 100 Hz is not considered.

To improve this situation, an extensive theoretical investigation was performed at PTB. Starting point was the idea to determine the unknown sound power level of a source, by substitution with another source of known sound power level. This was investigated in free field (no reflecting planes), but also in the vicinity of a single acoustic reflecting plane. The effect of the reflecting plane was modelled by both simple mirror sources, and the physically more correct superposition of many spherical waves.

It could be confirmed that the sound power level emitted from a source is altered by the presence of the acoustically reacting plane. It could be furthermore shown that the application of the substitution method leads to the sound power level that would be emitted into a free sound field. A fundamental precondition is, however, that both sources are of the same radiation order, i.e. monopoles are substituted by monopoles or dipoles by dipoles. In addition, it turned out that using sound intensity instead of sound pressure in the required measurements improves the approximation of the free field sound power level.

Fig. 1: Deviation of the sound power level using the substitution method from the corresponding free field sound power using sound pressure (black) and sound intensity (grey) levels. The deviation is plotted against the generalised quantity of kr, which combines all frequencies of interest with many measurement radii.

Therewith, foundations were established to apply the metrological principle of traceability to the sound power level. This will enable measurements at low frequencies, better characterisation of the occurring uncertainties and their long-term reduction.

### Literature:

Spyros Brezas, Martin Schmelzer, Volker Wittstock: Theoretical Investigation on the Sound Power Substitution Method. Acta Acustica united with Acustica 105 (2019) 426 – 434. DOI

### Contact:

Spyros Brezas, FB 1. 7, AG 1. 72, E-Mail: spyros.brezas(at)ptb.de