Delay Loudspeaker Time and Haas Offset

The delay time to set on a delay tower or under-balcony loudspeaker, and how far that setting moves when the air temperature does. The geometric half is the easy half: sound from the main array reaches the delay position some milliseconds after the delay speaker could fire, and delaying the tower by that time puts the two arrivals on top of each other. But two coincident arrivals from two directions do not localize, so the audience hears the delay speaker sitting right above them and the show appears to come from the wrong place. The Haas offset is the fix: adding 10 to 20 milliseconds beyond the geometric time makes the main array arrive FIRST by a margin the ear reads as the source direction, while the delay speaker, arriving inside the precedence window, still adds level without being heard separately. Fifteen milliseconds is the common starting point. Temperature is the trap, because the speed of sound rises with the square root of absolute temperature: a tower 180 ft downfield aligned at 70 F takes 160.0 ms of geometric delay, and on a 90 F afternoon the air carries sound at 1146 ft/s instead of 1125 and the geometric time falls to 157.1 ms. Three milliseconds is small, but the same twenty-degree swing on a 400 ft throw is 6.5 ms, which is audible, and outdoor shows re-check delay times when the air moves. An alignment starting point; a measurement system and the system engineer's ears govern the final setting.

c = 1125 x sqrt((temp_f + 459.67) / 529.67); geometric_ms = distance_ft / c x 1000; set_delay_ms = geometric_ms + haas_offset_ms.

Geometric propagation delay plus a Haas (precedence-effect) offset, with the speed of sound scaled as the square root of absolute temperature from the 1125 ft/s reference at 70 F, by name; the precedence effect is Haas's published result, cited not reproduced, and a measurement system and the system engineer govern the final setting.

Propagation delay and the temperature scaling of the speed of sound are public physics. The distance, temperature, and chosen Haas offset are the engineer's own values.

Estimate. AHJ and licensed professional govern.

Field names used by the API: distance_ft, temp_f, haas_offset_ms, compare_temp_f, speed_ft_s, geometric_ms, set_delay_ms, compare_geometric_ms

• Speed of sound 1125 ft/s at 70 F, scaled as the square root of absolute temperature (Rankine)physical acoustics
• Haas offset 10 to 20 ms beyond the geometric time; 15 ms is the common starting pointthe precedence effect (Haas)
• Temperature drift the error scales with distance, so long throws re-check when the air movesoutdoor system-engineering practice