Sound concentration caused by curved surfaces

In room acoustics the focusing effect of reflections from concave surfaces is a well known problem. Although curved surfaces are found throughout the history of architecture, the occurrence of concave surfaces has tended to increase in modern architecture, due to new techniques in design, materials and manufacturing. Among other things, focusing can cause high sound pressure levels, sound coloration or an echo. Although the problem is known, the amount of amplification that occurs in the focusing point and the sound field around the focusing point are not. It has been found that geometrical methods cannot be used to calculate the sound pressure in the focusing point. This pressure can only be calculated using wave based methods. This work provides mathematical formulations for sound reflections from concave surfaces, based on the Kirchhoff Integral. This method is verified with an experiment. An engineering method is given to approximate the sound field in and around the focusing point. This enables designers to evaluate and thereby improve or redesign the geometry. In the focusing point the pressure depends on the wavelength. The width of the peak pressure is also related to the wavelength. For small wavelengths the amplification is high but the focusing area is small, while for lower frequencies the amplification is lower, but the focusing area is larger. The focusing caused by surfaces that are curved in two directions (sphere, ellipsoid) is much stronger than that caused by surfaces that are curved in only one direction (cylinders). Generally, the possible reduction of the focusing effect that can be achieved by using absorbers or diffusers is not enough to eliminate the focusing effect of double curved surfaces. However, these methods might be sufficient to reduce the focusing caused by single curved surfaces such as cylindrical shapes. If absorption or diffusion is not sufficient, designers can consider either redirecting the reflections or more drastically revising the geometry. It would be preferable to consider the focusing caused by concave surfaces from the early design stages.