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 Paper VII · Its section on the reference page
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
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.
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.
ISO 3382-1:2009 — measurement of room acoustic parameters
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.
Background: Reverberation · Wallace Clement Sabine