Laboratory measurements of building acoustics at low frequencies: a modal approach

The current international request to extend standard laboratory measurements of building acoustics (airborne and impact sound insulation and reverberation time) to frequencies below 100 Hz requires a deep study on the involved physical phenomenon and a proper procedure in order to get repeatable and reproducible results. In typical laboratory volumes (50-80 m$^3$) and at low frequencies (50-100 Hz), the acoustic field is non-diffuse due to the presence of standing waves or resonant modes in the small laboratory rooms. In space and frequency domains, the sound field is characterized by large fluctuations of sound pressure levels, different from diffuse field condition, characterized by uniform sound field in both domains and is assumed from 100 Hz on in laboratory standard procedures. Under such conditions, standard sound insulation measurements and reverberation time descriptors are not adequate to correctly characterize the insulating property of partitions or flooring systems or the reverberation times of laboratory (or ordinary dwelling) rooms. For this reason, a new measurement approach based on resonant frequencies, or room modes, the so-called modal approach, is introduced. Resonant modes provide deterministic quantities in non-diffuse field and are responsible of most annoyance. For airborne sound insulation, the standard sound reduction index is not representative of sound insulation as it is based on sound power measurements, which is still undefined for non-diffuse acoustic field. In the coupled system room-partition-room, in addition to natural resonant modes of each system component, the transmission of modes from the source to the receiving room is observed. The modal approach allows to evaluate the sound insulation by the determination of the sound transmission loss of a single source room mode passing into the receiving room through the partition. Such characteristic is the base of the new descriptor: the modal sound insulation. It is defined as the difference between the maximum sound pressure levels (evaluated in the corners of rectangular rooms) of source room modes that occur in both source and receiving rooms. Starting from the classical modal theory, a proper normalization term, corresponding to receiving room volume, is also introduced and presented together with a new method, based on the envelope of room frequency responses, to extend the results to the whole low frequency range, due to the discrete nature of modal sound insulation. Furthermore, the uncertainty budget is analysed. From scale model measurements, normalization term results to be negligible and problems due to source and receiving room modal match, cause of sound insulation underestimation, has to be solved in the future with a proper weighting procedure, based on the increase of modal sound insulation as function of modal overlap degree (Kohlrausch-Williams-Watts function), experimentally evaluated in the scale model. The modal approach is also applied to impact sound insulation and impact noise reduction measurement: new procedure and descriptors are introduced and first experimental tests on three different mass-spring systems are shown. Results agree with theoretical basis and validate such approach. In the end, the modal approach is used for the measurement of reverberation time in small rooms, in terms of modal reverberation time. Two different methods are evaluated on the base of their mathematical relation: the direct and indirect methods. The first is based on the measurement of the direct modal sound decay, whereas the second evaluates the modal decay starting from the measurement of the half bandwidth of the resonant peak. For both methods, different sound signals are compared and suitable procedures are applied. First experimental tests show a good agreement between the two methods and their mathematical relation is confirmed.