Parameters influencing low frequency impact sound transmission in dwellings A. Neves e Sousa a , B.M. Gibbs b,⇑ a ICIST, DECivil, IST, University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal b Acoustics Research Unit, School of Architecture, University of Liverpool, Liverpool L69 3BX, UK article info Article history: Received 12 June 2013 Received in revised form 15 October 2013 Accepted 30 October 2013 Keywords: Impact sound transmission Low frequency Floors Dwellings Variance abstract As sound and vibration fields in dwellings exhibit modal behaviour at frequencies below 200 Hz, a sys- tematic investigation of measurement and prediction uncertainty associated with impact sound trans- mission at low frequencies must include the effects of: location of the impact, type of floor, edge conditions, floor and room dimensions, room absorption and position of the receiver. Experimentally val- idated analytical models, described in a companion paper, have been used in an extensive investigation of impact sound transmission through rectangular homogeneous concrete floors and floating floors. The models were used to describe the effect of modal coupling and then to perform parametric and statistical studies aimed to identify the main factors affecting low frequency impact sound transmission. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction In measurement and prediction of airborne and impact sound transmission at mid and high frequencies, typically above 200 Hz, diffuse field conditions often are assumed, particularly for the sound pressure in rooms. The standard methods are based on spatial averages and the effects of room dimensions (other than room volume), placement of absorption and receiver location are not considered [1–4]. Similarly, for impact sound transmission, vibration fields are assumed diffuse, thus neglecting the effects, on sound pressure, of the location of the impact, and the size and edge conditions of the floor [5]. Typically, at frequencies below 200 Hz, the sound and vibration fields in dwellings exhibit modal behaviour and a systematic inves- tigation of measurement and prediction uncertainty therefore must include the following factors: location of the impact; floor construction, material properties, dimensions and edge conditions; room dimensions, surface absorption, and listener/microphone location. A set of experimentally validated analytical models [6] have been developed to allow rapid repeated calculation, necessary for the parametric and statistical surveys reported in this paper. One of the models uses natural mode analysis to predict the point mobility of homogeneous rectangular floors, which can be combined with floating floors. Natural mode analysis also is used in a floor-room model of the pressure field generated by a vibrating floor in the room below. One of the main advantages of using analytical models is that they highlight the physics of the studied phenomena, which applies, in the present case, to the effect of modal coupling at low frequencies. 2. Modal coupling As described in a companion paper [6], the sound pressure field in a rectangular room, generated by a vibrating floor above, is given by pðx; y; z; tÞ¼jxq 0 X 1 l;m;n¼1 c 2 0  ð1Þ l  C mn  u lmn ðx; y; zÞ ½ðx lmn þ jdÞ 2  x 2 K lmn  e jxt ðPaÞ; ð1Þ where x (rad s 1 ) is the angular frequency of the sound wave; c 0 (m s 1 ) is the phase velocity of sound in the air; q 0 (kg m 3 ) is the static value of air density; u lmn (x, y, z) and x lmn are, respectively, the eigenfunctions and corresponding eigenvalues of a rectangular room of volume V = abc (m 3 ) according to Fig. 1; K lmn = R u lmn (x, y, z) 2 dV; d is a temporal absorption coefficient which is a func- tion of the room reverberation time T r (s), according to d = 6.9/T r [7]; and C mn are coupling factors depending on the vibration velocity distribution on the floor. For a point excited simply supported plate, the coupling factors C mn are expressed as: 0003-682X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apacoust.2013.10.013 ⇑ Corresponding author. E-mail address: bmg@liverpool.ac.uk (B.M. Gibbs). Applied Acoustics 78 (2014) 77–88 Contents lists available at ScienceDirect Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust