From Nature and Basic Scientific Results to Modern Engineering Applications

From Nature and Basic Scientific Results to Modern Engineering Applications

Giora Rosenhouse

Swantech Ltd. Haifa, Israel Technion, Haifa, Israel (Retired Prof.)

Available online: 
| Citation



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.


[1] Rosenhouse, G., The acoustical comfort and speech privacy in the design of flexible open-plan offices. 42th Inter-noise Conference, Innsbruck, 15–18 September, 2013, presentation #140, 2013.

[2] Rosenhouse, G., The spectral effect of masking of intruding noise by environment background noise. 167th Meeting of the Acoustical Society of America, Providence, Rhode Island, 5–9 May, 2014.

[3] Rosenhouse, G., The spectral effect of masking of intruding squeal noise by environmental background noise – A detailed analysis. Spring 2016 Meeting of the Acoustical Society of America, Salt Lake City, Utah, 23–27 May, 2016.

[4] Rosenhouse, G., The subjective analysis of wheel-rail squealing noise by modification of the British standard BS4142:2014, Inter Noise 2018, Chicago, Illinois, 26–29 August 2018, Presentation 1887 (On USB Device), 2016.

[5] BS4142:1997, Method for Rating Industrial Noise Affecting Mixed Residential Areas and Industrial Sites, British Standards Institution, BSI, London, 1997 and BS4142:2014, Method for Rating and Assessing Industrial and commercial sound, British Standards Institution, BSI, London, 2014.

[6] ISO 1996, Assessment of Noise with Respect to Community Response -International Organization of Standardization, Geneva, 1971; (see also 1982–1987, 1998).

[7] ANSI S3.5-1997, Methods for calculation of the speech intelligibility Index, American National Standard, Standards Secretariat, Acoustical Society of America, NY, 1997

[8] ASTM E 1130 – 02, Standard Classification for Determination of Articulation Class, American Society for Testing and Materials, 2001.

[9] Mayer, A.M., Researches in acoustics, Philosophical Magazine, 2, pp. 500–507, 1876.

[10] Fletcher, H., Auditory patterns, Reviews of Modern Physics, 12, pp. 47–65, 1940.

[11] Fletcher, H., Speech and Hearing in Communication, ASA, NY, pp. 153–175, 318–414, 1995. Originally published by van Nostrand, NY 1953.

[12] Rosenhouse, G., Finite sound barriers and the use of Heron’s formula. INTER-NOISE 2009, Ottawa, Canada, August 23–26, 2009. See also, G.Rosenhouse, The use of the simplex approach for analysis of infinite and finite sound barriers. Inter-Noise 2019, Madrid, Spain, 16–19.July, 2019, Presentation 1555 (On USB Device)

[13] Maekawa, Z-I., Noise reduction by screens. Journal of Applied Acoustics, 1, pp. 157–173, 1968.

[14] Pierce, A.D., Diffraction of sound around corners and over wide barriers. Journal of the Acoustical Society of America, 55(5), pp. 941–955, 1974.

[15] Hitzer, E., Introduction to Clifford’s geometric algebra. SICE Journal of Control, Measurements and System Integration, 4(1), pp. 1–11, 2011.

[16] Dantzig, G.B., Origins of the Simplex Method, Technical Report, Stanford University Systems Optimization Lab, 87–5, 1987.

[17] Hardy, G.H. & Wright, E.M., (Reviewed by: D.R., Heath-Brown, D.R., Silverman, J.H., Wiles, A.), An Introduction to the Theory of Numbers, 6th ed. Oxford University Press, NY, USA, 2008.

[18] Schroeder, M.R., Diffuse sound refection by maximum length sequences. Journal of the Acoustical Society of America, 57, pp. 149–150, 1975.

[19] Schroeder, M.R., Binaural dissimilarity and optimum ceilings for concert halls: More lateral sound diffusion. Journal of the Acoustical Society of America, 65(4), pp. 958–963, 1979.

[20] Cox, T. & D’Antonio, P., Acoustic Absorbers and Diffusers: Theory, Design and Application, Spon Press: London and New York, 2004; Tailor & Francis, 2nd ed. 2009.

[21] ISO 17497-1:2004 – Acoustics – Sound scattering properties of surfaces. Part 1: Measurement of the random – incidence scattering coefficients in a reverberation room.

[22] ISO 17497-2:2012 – Acoustics – Sound scattering properties of surfaces. Part 2: Measurement of the directional diffusion coefficient in a free field.

[23] Schroeder, M.R., Die statistischen Parameter der Frequenzkurve von großen Räumen. Acustica, 4, pp. 594–600, 1954. [English translation: M. R. Schroeder, Statistical parameters of the frequency response curves of large rooms. Journal of Audio Engineering Society, 35, pp. 299–306, 1987. Note: In the original 1954 paper a more conservative factor of 4000 was proposed instead of 2000 in Eq. corresponding to a tenfold mod.

[24] Schroeder, M.R., Sequences from number theory for physics, signal processing and Art. Acoustical Physics, 49(1), pp. 97–108, 2003.

[25] Bragg, W.H., X rays and crystals. Nature, 90, p. 219, 1912.

[26] Bragg, W.H., X rays and crystals. Nature, 90, pp. 360–361, 1912.

[27] Bragg, W.L., The diffraction of short electromagnetic waves by a crystal. Proceedings of the Cambridge Philosophical Society, XVII, 1913.