Near-field tangential particle velocities: Piston radiator vs. QRD phased linear array

Loudspeakers in cars are constrained in size and placement. As such, near-field and mid-field sound properties are of interest. The near-field of a circular piston in an infinite baffle is well studied, and often used as an approximate model for a loudspeaker. Whilst a piston's SPL directivity pattern is well understood, its polar pattern of particle velocity direction has received less attention. We calculate the radial and tangential components of the piston model's particle velocity field, and find that tangential velocity dominates at particular angles for a given piston frequency. These polar positions relate to the 'dips' in the SPL directivity pattern. Contrasting these results with the sound-field of a linear array of spherical sound sources having phase delays determined by a QRD sequence, we find the QRD array yields greater uniformity in both SPL directivity and particle velocity direction.