Loudness perception requires a tenfold intensity increase to double

Evidence

The results typically lie close to a straight line whose gradient is a doubling in loudness for 10 dB(SPL) variation from around 40 dB(SPL)—a result that is somewhat surprising, perhaps, since a doubling in intensity is a +3 dB change and a doubling in pressure is a +6 dB change. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 652

Categorization

• XREF: This Steven’s-power-law fact — loudness doubling for 10 dB — is a classic surprising psychoacoustic nugget everyone from musicians to audio engineers misunderstands. — connects to: Doubling perceived loudness requires a 10 dB increase. — Toole, Floyd E, Sound reproduction- the acoustics and…, 889; Loudness grows as a power law of physical intensity so relative changes match — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1262; A tenfold intensity increase is perceived as only twice as loud — Eric J. Heller, Why You Hear What You Hear- An…, 143 (+13 more)
• CANDY: A small counterintuitive fact: your ears need a 10 dB jump to hear something twice as loud, though 3 dB already doubles physical energy.
• QUESTION: Why is the correspondence nonlinear — what evolutionary or physiological constraint makes perceived loudness compress physical range this way?
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 652

Broader Connections

• Perceived loudness and physical sound intensity follow different, non-intuitive mathematical scales #expands (0.88) — George Michelsen Foy, Zero Decibels, 53
• Spreading a sound’s energy across more critical bands increases perceived loudness without raising intensity #qualifies (0.82) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 665