Long before audio technologists have been researching the acoustic reproduction of entire sound fields using loudspeaker arrays, numerical acousticians began to study the solution of boundary integral equations. This is particularly interesting because the fundamental question of uniqueness also appeared in numerical acoustics much earlier than it recently did in the theory of sound field synthesis, where it still appears to be pending. There were two main approaches that proved non-uniqueness at certain frequencies to be soluble by enforcing all the necessary mathematical constraints. Both are directly applicable to generally ensure uniqueness in the sound field synthesis theory based on free field monopole sources.
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