Loudness and intensity

Beginner

Perceived loudness relates to intensity logarithmically.

Loudness is perceived and roughly logarithmic in intensity; physical intensity I = P/A in W/m². The ear can handle 10⁻¹² to 1 W/m².

Worked example

A jet engine at 100 m has I ≈ 1 W/m².

Common mistake

Loudness also depends on frequency.

In more detail

Loudness is our perception of sound strength, which depends on intensity but is nonlinear. Doubling intensity does not double perceived loudness.

Concert halls and cinemas set sound levels for comfort and safety.
Hearing protection is rated by decibels of attenuation.
A sound meter shows that doubling the intensity does not double the perceived loudness, which is why a logarithmic scale is used.

Why is loudness nonlinear?

The ear responds to intensity logarithmically, so equal ratios sound like equal steps.

Does loudness depend on frequency?

Yes. The ear is more sensitive around 2 to 4 kHz than at very low frequencies.

Why is loudness not linear with intensity?

Human hearing responds roughly logarithmically, so equal steps in loudness correspond to equal ratios in intensity.