Mathematically trivial control of sound using a parametric beam focusing source

By exploiting a case regarded as trivial, this paper presents global active noise control using a parametric beam focusing source (PBFS). As with a dipole model, one is used for a primary sound source and the other for a control sound source, the control effect for minimizing a total acoustic power depends on the distance between the two. When the distance becomes zero, the total acoustic power becomes null, hence nothing less than a trivial case. Because of the constraints in practice, there exist difficulties in placing a control source close enough to a primary source. However, by projecting a sound beam of a parametric array loudspeaker onto the target sound source (primary source), a virtual sound source may be created on the target sound source, thereby enabling the collocation of the sources. In order to further ensure feasibility of the trivial case, a PBFS is then introduced in an effort to meet the size of the two sources. Reflected sound wave of the PBFS, which is tantamount to the virtual sound source output, aims to suppress the primary sound. Finally, a numerical analysis as well as an experiment is conducted, verifying the validity of the proposed methodology.