Collegium Omnium Mentium

The College of All Minds

Manent et numerantur

Sabine’s reverberation equation and its failing assumptions

PAPER VII — ENGINEERING · QUESTION 31 OF 32

In plain terms: The free demonstration of the picture behind the equation, before the algebra.

The question as set

Derive Sabine’s reverberation equation, state the assumptions that fail in a real hall, and say what a modern hall does about them.

The question in context

This is question 31 of the 32 set in Paper VII — Engineering of The Truly Hardest Exam in the World, the examination of The College of All Minds. In the College’s subject index it is filed under Acoustics. Like every question of the College, it carries three references of record, verified live at publication and described twice — technically, and in plain terms — so the ground can be judged before it is walked. The response required is an argument, not a survey, of at most three thousand words, as technical as the question demands and no more.

The references of record

Reverberation — demonstrations D. A. Russell · current · Penn State

The diffuse-field model illustrated: mean free path, absorption per reflection, and the exponential decay Sabine’s formula assumes.

In plain terms: The free demonstration of the picture behind the equation, before the algebra.

D. A. Russell (page)

Reverberation J. O. Smith III · current · Physical Audio Signal Processing (free edition)

The derivation and its limits: RT₆₀ = 0.161V/A, with the diffuse-field and uniform-absorption assumptions each identified.

In plain terms: The free Stanford text deriving the formula and stating plainly where it stops being true.

J. O. Smith III (page)

ISO 3382-1:2009 — measurement of room acoustic parameters ISO · 2009 · iso.org

The parameters a modern hall is actually designed to: EDT, clarity, lateral fraction — the quantities Sabine’s single number omits.

In plain terms: The free catalogue record of the standard that replaced one number with several.

International Organization for Standardization

Background: Reverberation · Wallace Clement Sabine

Download Paper VII (Markdown) · Subject index