Comparison of sound reproduction using higher order loudspeakers and equivalent line arrays in free-field conditions

Higher order sound sources of Nth order can radiate sound with 2N + 1 orthogonal radiation patterns, which can be represented as phase modes or, equivalently, amplitude modes. This paper shows that each phase mode response produces a spiral wave front with a different spiral rate, and therefore a different direction of arrival of sound. Hence, for a given receiver position a higher order source is equivalent to a linear array of 2N + 1 monopole sources. This interpretation suggests performance similar to a circular array of higher order sources can be produced by an array of sources, each of which consists of a line array having monopoles at the apparent source locations of the corresponding phase modes. Simulations of higher order arrays and arrays of equivalent line sources are presented. It is shown that the interior fields produced by the two arrays are essentially the same, but that the exterior fields differ because the higher order sources produces different equivalent source locations for field positions outside the array. This work provides an explanation of the fact that an array of L Nth order sources can reproduce sound fields whose accuracy approaches the performance of (2N + 1)L monopoles.