Acoustic Propagation Velocity, 3D Slant Geometry & Haas Precedence

In large-scale live sound reinforcement, acoustic energy travels through air as a longitudinal pressure wave at a finite velocity $c$ (~343 m/s at $20^\circ\text{C}$), whereas the electrical audio signal reaches remote delay amplifiers through copper or fiber-optic trunks near the speed of light. Without digital signal delay ($t_{\text{DSP}}$), audiences standing behind a delay tower hear the delay speaker tens of milliseconds before the main FOH array arrives, resulting in distinct slapback echoes and severe comb filtering.

Furthermore, because main line arrays are flown at trim height $h_{\text{main}}$, the true acoustic propagation distance to a listener at horizontal distance $d_{\text{main}}$ follows the Pythagorean slant hypotenuse $D_{\text{slant}}$, rather than flat ground distance. After aligning arrival times geometrically, FOH engineers frequently add $5\text{ ms}$ to $15\text{ ms}$ of extra Haas Precedence delay so the listener’s auditory cortex continues to localize the sonic image toward the stage rather than up at the nearest fill cabinet.