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Can the sound reduction index of buildings also be applied to low frequencies?


Noise at low frequencies is constantly increasing. The characteristic quantity for protection against noise – the sound reduction index – has, however, not been defined for this range. It has therefore been investigated as to whether it is nevertheless applicable to low frequencies.

Increasing road traffic, the improved audio-equipment of our next-door neighbours, as well as aggregates for an efficient energy generation which get increasingly close to our dwellings (including wind energy plants) generate – to an ever increasing extent – noise which reaches down to very low frequencies (1 Hz). It is therefore necessary to define noise protection of buildings also at low frequencies. The characteristic quantity prescribed for this purpose by the building inspection authorities is the sound reduction index. This index can, however, be applied only to frequencies above 100 Hz. (This results unavoidably from the desire to treat the sound reduction indices of the elements of a building – or of a type of construction in general – like a material property which can be determined in advance in a laboratory and which will then be found in any building whatsoever, regardless of its dimensions). As far as this desire can be fulfilled at all, it requires a uniform distribution of the sound fields in the rooms (so-called "diffuse" sound fields). Such a distribution is given, however, only as long as the wavelengths involved are much smaller than the relevant geometrical dimensions, i. e. from 100 Hz upwards, at the earliest. In view of the increasing noise load and of the public's need for protection against noise, it would, however, not be sufficient to just not take the low frequencies into account. How the noise reduction index behaves outside its definition range down to the frequency zero was, therefore, investigated. For this purpose, a one-dimensional arrangement of two rooms with a sound insulating wall between them has been assumed. The calculation comprised, on the one hand, the acoustic powers which impinge on the wall respectively pass through it – in order to form the sound reduction index – and, on the other hand, the sound pressures in the rooms –  because it is these which are perceived by the human ear. The model intended to show the influence which the individual room modes – which become apparent ever more clearly with decreasing frequency – seemingly exert on the sound reduction index of the wall and thus make the same not only hardly predictable in each individual case, but also uncertain with respect to the requirements to be met. In addition, it has been investigated as to what extent "weak points" of the sound reduction of the building elements are modified by the modal room sound fields at low frequencies. For this purpose, a double wall with a thickness resonance of 50 Hz has been investigated as a separating element, in addition to a homogeneous single wall. The computation model used was again one-dimensional. Effects in transverse direction – such as, for example, coincidence of airborne and structure-borne sound fields – have so far not been taken into account. The calculations yielded the following: The properties of the "emission room" (in which the sound source is located) do not influence the sound insulation, as only the power that impinges on the wall is to be taken into account. The airborne sound modes of the receiving room can be seen as strong dips in the sound insulation (see Figure 1). These dips represent actual changes in the sound insulation and are not, as has been assumed so far, an uncertainty of the measurement of an actually unchanged  ("characteristic") sound insulation of the wall due to the very non-uniformly distributed sound pressures at low frequencies. At very low frequencies – in Figure 1 at approx. 5 Hz – there is a resonance from the partition wall mass and the stiffness of the air spring of the receiving room which has so far not been taken into account. In this frequency range, the sound pressure in the receiving room may become larger than in the emission room, although the exactly calculated power ratio yields positive sound insulation values.

Figure 1. Sound reduction index R of a single wall, area-related mass: 40 kg/m².
Broken line: Theoretical curves for an infinite wall without adjacent rooms.
Length of  emission room: 3 m. Length of receiving room: 3 m.

Figure 2 – in which the sound insulation spectrum of a double wall is represented for receiving room depths from 2.5 to 15 m – finally shows that the adjacent rooms practically do not exert any influence on the break at the resonance frequency. The investigations show a first indication as to which effects will have to be taken into account if, in future, a concept for a sound reduction index will be developed which will provide reasonable values – i. e. values which are in accordance with the perception – also at lowest frequencies. At present, the question as to what extent very low frequencies are perceived by humans is still the subject of research.

Figure 2. Sound reduction index R of a double wall (resonance frequency: 50 Hz) for receiving room lengths from 2.5 to 15 m.
Red line = averaged curve.
Thin green lines = theoretical curves according to L. CREMER for infinite walls without rooms.

Contact person:

Werner Scholl, Dept. 1.7, e-mail: werner.scholl@ptb.de