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The Directional Scattering Coefficient: Experimental Determination

The purpose of this paper is to suggest an experimental procedure to determine the directional scattering coefficient (DSC) or directivity balloon which fully represents the backscattered energy from any acoustical surface as a function of the incident frequency and direction. For absorbing materials, this directional information complements the random-incidence absorption coefficients, determined using the ASTM reverberation chamber method, and upon appropriate integration should also yield the random-incidence value. In the case of reflecting, diffusing and diffracting surfaces these data will begin to fill a void in the acoustics literature. The DSC is necessary in the design of critical listening and performance environments where strategic rather than statistical application of acoustical materials is desired. Also a directional, rather than a random-incidence, scattering parameter is of more significance in the various image and ray tracing computer room modeling programs to improve the accuracy of impulse response predictions and auralizations, derived from convolutions of anechoic program material with these impulses. It is hoped that the suggestions made in this paper will eventually lead to an ASTM standard and that these data will improve the accuracy of predictive as well as actual acoustical designs. As a first step the time, frequency and polar energy response of flat panels, with and without distributed absorption, mono- and bicyclindrical columns and reflection phase grating diffusors have been measured, using a boundary measurement technique based on time-delay spectrometry, which allows measurement of the DSC in two orthogonal planes. Energy-time curves, directivity-energy-frequency curves, frequency-directivity contours and conventional octave-averaged polar patterns are presented for 0 degrees and 45 degrees incidence. A specularity index was developed to compress the directional data into a useful parameter which reflects the laterally scattered energy over a 90 degrees solid angle compared with the specular direction. A new automated polar mapping technique, which is capable of yielding the full 3-D directivity balloon, is suggested. The sound source is placed on the floor boundary, a hemispherical or flat grid of appropriately spaced microphone locations is sampled above this at approximately 15 feet and the sample surface of appropriate size is suspended 15 feet above the microphone grid. The microphone locations collect the backscattered response at an appropriate angular increment for each angle of incidence. These data are then analyzed and the ratio of the free field backscattered power and the appropriately scaled incident power yields the DSC.

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