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J. Acoust. Soc. America, 62 (1977) 1436. Proceedings of the Vancouver Symposium, Acoustics and Theatres for the Performing Arts, The Canadian Acoustical Association, Ottawa, Canada, 1986, p. 112. Reflection and scattering 31 2 Reflection and scattering Up to now we have dealt with sound propagation in a medium which was unbounded in every direction. In contrast to this simple situation, room acoustics is concerned with sound propagation in enclosures where the sound conducting medium is bounded on all sides by walls, ceiling and floor.

In the following it is convenient to use a spherical polar coordinate system as depicted in Fig. 9. Its origin is the centre of a wall element dS, the wall normal is its polar axis. We consider an element of solid angle dΩ around a direction which is determined by the polar angle Θ and the azimuth angle Φ. Expressed in these angular coordinates, the solid angle element is dΩ = sin Θ dΘ dΦ. First we calculate the dependence of the energy density, which is essentially equal to the square of the sound pressure amplitude, on the distance from the wall which, for the moment, is assumed to be perfectly rigid (R = 1).

E. 8 (a) Locus of the wall impedance in the complex impedance plane for resonance system. (b) Ratio of velocity to pressure amplitude as a function of the driving frequency for a resonance system. 30) has been introduced. Assuming that δ is small compared with ω 0, ω1,2 = ω 0 ± δ are the angular frequencies for which the phase angle of the wall impedance becomes ±45°. At the same time the value of the velocity amplitude at these Reflection and scattering 45 frequencies is below the maximum value S/2δ M by a factor (2)1/2.

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