Acoustic scattering for a hard hemisphere on a hard plane - Measurements and theory for applications in room acoustics

Report, 2005

Scattering from a hemisphere placed on an infinite plane is studied theoretically and experimentally in a laboratory environment. Green's function for homogeneous Neumann boundary conditions is determined theoretically with the boss model – a combination of the method of images, principle of superposition, and separation of variables. This implies that the transducers are point-like and omni-directional with flat frequency spectrum, and that the normal component of the particle velocity is zero on all boundaries. In an experimental set up, none of these conditions are perfectly fulfilled. The directivity of the loudspeaker was measured and compensated for in the theoretical model, while remaining discrepancies between experiments and model are discussed. Scattering for different combinations of transducer and hemisphere positions are classified into a number of cases, denoted on-axis/off-axis, back/forward, and specular/non-specular. Results are compared and evaluated from an auralization point of view using 1/3 octave band level smoothing of the contribution from the hemisphere. With the smoothing used, average discrepancies less than 3 dB are obtained for ka-values between 1 and 32, where a equals the hemisphere radius. This work would not have been possible without the research funding provided by Vetenskapsrådet. The authors are also indebted to Christopher C. Cichetti, Jovanie Zayas at Worcester Polytechnic Institute who performed all the measurements during their stay at the department, and their major advisor, Professor Richard H. Campbell.