Sound Reflections from Concave Spherical Surfaces. Part I: Wave Field Approximation

Abstract

Focussing arising from reflections at concave surfaces is a well-known problem in room acoustics. Focussing can cause high sound pressure levels, colouration or an echo. Although the problem is known, the amplification in the focal point and the sound field around the focal point are not. This paper provides some mathematical formulations for sound reflections from concave spherical surfaces. The formulation is based on a wave extrapolation method. The approximations given can be used to calculate the sound field in and around the focal point. The calculation method is verified with an experiment. In the focal 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 area is small, while for lower frequencies the amplification is less, but the area is larger. In a second part of this paper [1] geometrical and engineering methods will be discussed for describing the focussing effect.