WIT Press

From nature and basic scientific results to modern engineering applications


Free (open access)


Volume 14 (2019), Issue 4



Page Range

249 - 263

Paper DOI



WIT Press


Giora Rosenhouse


The motto of the paper concerning physics and nature is a quotation by Eugene Wigner: ‘The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve’. The first case in this paper is based on an original paper by this author, and it uses Fletcher’s scale of speech intelligibility, for analysis of specific noise effect in the presence of background noise. The idea is based on the assumption that the brain uses the same scale for estimating both intelligibility and nuisance by specific noise. This notion was confirmed by experiments. The second case below is the use of the ‘simplex theory’, which is a mathematical model used in computer sciences, and was published originally by this author as a means for design of environmental sound barriers. The third application involves sophisticated use of specular reflections and scattering in acoustics, with application of acoustic quadratic residues in interiors acoustics, based on the mathematical theory of numbers, where prime numbers are involved. Leading mathematicians in this development are Euclid (325 BC–265 BC) and Gauss (1777–1855), who discovered in the 18th century quadratic residues. In the context of diffraction physics, the main contribution was by Röntgen (1845–1923), von Laue (1879–1960), W.H. Bragg (1862–1942), and W.L. Bragg (1890–1971). This long way towards sophisticated acoustic diffusers that turn specular reflections into a uniform diffusion needed one more leading physicist to make the breakthrough. Manfred Schroeder (1926–2009) published a seminal paper in 1975, adding the number theory to room acoustics as a legitimate part. He has proved mathematically that specific panels with a sequence of one-dimensional or two-dimen- sional grooves result in a diffusive-phase grating of wide band, instead of a specular reflection panel. This result was directly applicable from the theory of x ray diffraction. D’Antonio and Cox continued improving the results, leading to special quadratic residue diffuser (QRD) shapes. Many of the panels resemble shapes that exist in nature.


BS 4142: 2014, outdoor noise control, physical innovations, primary numbers, quadratic reduced difftusors (QRD), scattering of sound, Simplex method, Sound Barriers, squealing noise, Subjective acoustics.