Angular Distribution Analysis in Acoustics by S. M. Baxter

By S. M. Baxter

The function of this booklet is to j.ir€'~ 0l'l\' a brand new approach for the experimental research of the loose wave version sound box of acoustics. The process is predicated at the use of round harmonic services of perspective. Acousticians often come upon random sound fields whose homes will be heavily modelled by means of use of the "free wave" box. This version box is outlined through easy statistical houses: stationarity in time, and homogeneity in house. Stationarity signifies that any unmarried order statistic measured through a microphone within the box can be self sufficient of the time at which the recording is taken, whereas homogeneity implies that the dimension can be self reliant of the mic- phone's place within the box. additionally, moment order information received from the measurements of 2 microphones will rely purely at the time lapse among the 2 recordings, and the relative spatial separation of the micro­ telephones, and never at the microphones' absolute positions in area and time. The loose wave box can also (equivalently) be pictured as a suite of airplane sound waves which method an commentary place from all angles. those are the "free waves" of the name, with out correlation among waves at diversified angles and frequencies, even though there may possibly exist an angle-dependant airplane wave density functionality. this can be a degree of the density of sound strength coming back from diversified angles. The unfastened wave box has proved to be an easy yet remarkably robust model.

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80 ) l: q=-~ A spherical harmonic series is to a function of angle what a Fourier series is to a periodic time series. 81) £=0 If the coefficients fq £ are chosen properly, then most approximated arbitrarily closely by a large enough series. functions can be This fact depends on a property of harmonics called "completeness", and to understand this properly some properties of functions of angle must be introduced. 82) exists, and "square integrable" if 'IT 6 exists. dv sin v 2 'IT I o du If(v,u) 12 A square integrable function is always integrable as well, but the converse is not necessarily true.

22). 53) is in general a weighted integral over plane wave angle. 31, Chapter 11) that w(p,v, e) = (1/1T) {(sin 8 sin v)2 - (cos e cos (v_p))2} -! This result holds provided the expression in curly brackets is positive; w is zero otherwise. 10). the property that the area under its graph as a It has function of cos v is 1, independently of the value of p. To interpret the properties of the window function, let an angle p cos ~ be defined by ~ so that Q may be written Q(W,8). 53) representing Q must be (w-e), since w is zero outside this interval, so that cos only waves from a restricted range of angles contribute to Q.

Journal of the Acoustical Society of America 48, 1-5 (1970). Discrete versus continuous space averaging in a reverberant sound field. , Journal of the Acoustical Society of America 43, 1436-1443 (1968). Statistical properties of reverberant sound fields. , Journal of the Acoustical Society of America 46, 277-283 (1969). Effect of frequency and space averaging on the transmission responses of multimode media. , WATERHOUSE, R. , Journal of the Acoustical Society of America 53, 650-659 (1973). Effectiveness of continuous spatial averaging in a-diffuse sound field.

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