10 th Convention of the European Acoustics Association Turin, Italy • 11 th – 15 th September 2023 • Politecnico di Torino POINT TO POINT PROPAGATION OVER PERIODIC ROUGH BOUNDARIES Keith Attenborough 1* Steve Mellish 1 Shahram Taherzadeh 1 Imran Bashir 2 Alex Stronach 3 1 School of Engineering and Innovation, The Open University, UK 2 School of Computing, Engineering and Digital Technology, Teeside University, UK 3 RPS Group, Manchester, UK ABSTRACT * A rough surface formed by regularly spaced acoustically hard parallel strips or grooves gives rise to non-specular diffracted modes and surface waves. Surface waves result in values greater than +6 dB in spectra of the sound field relative to the direct field (excess attenuation). As well as surface wave generation, measurements of excess attenuation over regularly spaced parallel strips show effects of the finite array dimensions. Numerical predictions of pressure contours at the frequency of main surface wave energy show that the surface waves are created by overlapping, interacting, quarter wavelength resonances in the gaps between roughness elements or within grooves. Additional peaks in EA spectra result from interference between surface waves and diffracted components travelling towards the source. Surface waves are reduced if roughness elements resonate at surface wave frequencies. Predictions over periodic rectangular grooves with the same width but depths varied to create a phase change of 2π over each period show non-specular behaviour associated with surface wave generation and diversion of energy into diffracted modes. Useful traffic noise insertion loss due to a periodic surface consisting of rectangular grooves with different depths is predicted. Keywords: surface waves, periodic roughness, quarter wavelength resonance, excess attenuation. ————————— * Corresponding author: keith.attenborough@open.ac.uk. Copyright: ©2023 Keith Attenborough et al. This is an open- access article distributed under the terms of the Creative Commons Attribution 3.0 Unported License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 1. INTRODUCTION The solution for the sound field due to a point source in air over a rough acoustically hard boundary, for which the roughness height and spacing are small compared with the incident wavelength, includes an airborne surface wave which spreads cylindrically but attenuates exponentially both away from and along the surface [1]. Surface waves of this kind have been observed in laboratory experiments over rectangular grooves at ultrasonic frequencies [2], and, at audio-frequencies, over rectangular lattices [3,4], regularly spaced parallel cylinders [5], triangular wedges [6,7], and square and rectangular strips [7,8]. Outdoor measurements have indicated airborne surface waves over regularly spaced, parallel rows of bricks [9,10]. Surface waves can be detected in either frequency or time domains. Point-to-point propagation near a surface can be represented by the excess attenuation (EA) spectrum defined by, (1) Over an acoustically hard smooth surface the excess attenuation spectrum has a maximum of +6 dB which represents pressure doubling due to constructive interference between direct and ground-reflected sound pressure fields. Effectively, a rough hard boundary has a finite impedance and thereby causes a dip in the EA spectrum associated with destructive interference between the direct wave and the specular component of the reflected wave at a lower frequency than over a smooth hard surface. If a surface wave is generated, then the maximum exceeds +6 dB around the frequency of maximum surface wave energy. A roughness-induced surface wave appears in the time domain as a wave train following the direct and reflected wave component arrivals. DOI: 10.61782/fa.2023.0092 5279