Potential / Needed Acoustic Gain (Feedback Stability)

Whether a sound system can get loud enough (NAG) before it feeds back (PAG).

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Details, formula, and sources

Whether a sound-reinforcement system can be loud enough (needed acoustic gain, NAG) before it rings (potential acoustic gain, PAG). PAG = 20log(D1) + 20log(D0) - 20log(Ds) - 20log(D2) - 10log(NOM) - 6, from the four critical distances (Ds talker-to-mic, D0 talker-to-farthest-listener, D1 speaker-to-farthest-listener, D2 speaker-to-mic), NOM open mics (each doubling costs 3 dB), and a 6 dB feedback margin. NAG = 20log(D0/EAD), the gain the back row needs over the unaided talker (EAD = equivalent acoustic distance). The system works when PAG >= NAG. Ds 2, D0 30, D1 8, D2 12 ft, 1 mic, 6 ft EAD -> PAG 14.0 = NAG 14.0, the textbook balance; moving the mic to 1 ft raises PAG to 20 dB. Get the MIC close to the talker, the SPEAKER close to listeners and away from the mic, and minimize open mics. A design screen; the room acoustics, mic/speaker directivity, and tuning govern actual stability.

pag_db = 20log(d1_ft) + 20log(d0_ft) - 20log(ds_ft) - 20log(d2_ft) - 10log(open_mics) - 6; nag_db = 20log(d0_ft / ead_ft); the system is workable when pag_db >= nag_db.

Potential and needed acoustic gain (PAG/NAG feedback-stability analysis; Davis & Patronis, Sound System Engineering; Yamaha Sound Reinforcement Handbook), by name; the actual room acoustics, the microphone and loudspeaker directivity, and the system tuning govern real-world stability.

The PAG/NAG relations are public sound-reinforcement engineering; the four distances, the open-mic count, and the equivalent acoustic distance are the system's layout values.

Estimate. Head rigger and manufacturer working-load-limit charts govern. Inspect every piece of hardware before the show.

Field names used by the API: ds_ft, d0_ft, d1_ft, d2_ft, open_mics, ead_ft, pag_db, nag_db, margin_db

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