Equal Loudness Curves

Two sounds with exactly the same physical intensity level can sound wildly different in loudness if they're at different frequencies. Equal loudness curves are the experimental record of exactly how the ear's sensitivity varies with pitch — and they're the reason dBA exists at all.

Producing the curves

The previous lesson defined intensity level, $IL$, as a purely physical quantity in decibels. But two sounds with identical $IL$ values don't necessarily sound equally loud if they're at different frequencies — the ear's sensitivity itself varies with frequency. Equal loudness curves are built to measure exactly how.

The standard procedure works like this:

• A reference frequency is chosen, conventionally 1 kHz, and a sound at that frequency is played at some fixed intensity level — this becomes the loudness benchmark for the whole curve.
• At many other frequencies spanning the audible range (roughly 20 Hz to 20 kHz), listeners are asked to adjust the intensity level of a test tone at that frequency until it sounds exactly as loud as the 1 kHz reference.
• The intensity level required at each frequency to match the reference loudness is recorded and plotted against frequency. The resulting curve — intensity level (dB) on the vertical axis, frequency on the horizontal, usually plotted on a logarithmic frequency scale — is one equal loudness curve: every point on it sounds equally loud, by construction.
• Repeating this whole process for reference tones at different starting loudnesses produces a family of equal loudness curves, one for each perceived loudness level, giving a complete map of how intensity level needed for a given loudness varies across both frequency and loudness itself.

Interpreting the shape of the curves

The single most important feature of an equal loudness curve is that it is not flat. If the ear were equally sensitive at every frequency, each curve would be a horizontal line — the same intensity level would be needed everywhere to sound equally loud. Instead, the curves dip down toward a minimum somewhere in the mid-frequency range (typically in the 2–5 kHz region, where the ear is most sensitive) and rise steeply at both the low-frequency and high-frequency ends of the audible range.

This shape means:

• In the mid-frequency region where the curve is lowest, relatively little intensity is needed for a sound to be perceived as loud — the ear is at its most sensitive here.
• At low frequencies (bass sounds) and very high frequencies (treble sounds), a considerably higher intensity level is needed to produce the same perceived loudness — the ear is much less sensitive at the extremes of its range.
• The gap between the curve's minimum and its value at the low- or high-frequency extremes can be tens of decibels, meaning a low-frequency sound may need to be physically far more intense than a mid-frequency sound just to sound equally loud.

Why dBA weighting exists

Because the ear's sensitivity depends so strongly on frequency, a single unweighted dB measurement of a sound doesn't reliably tell you how loud that sound will actually be perceived — two sounds with the same physical $IL$ but different frequency content can sound noticeably different in loudness, exactly because they sit at different heights on the equal loudness curve family.

dBA weighting exists specifically to correct for this. It applies a frequency-dependent adjustment to the raw physical intensity level, informed by the general shape of the equal loudness curves: frequencies where the ear is less sensitive (the low- and high-frequency regions where the curves rise steeply) are down-weighted less generously, while the correction is shaped so the final single-number reading tracks perceived loudness far better than an unweighted dB figure would. This is precisely why dBA, not plain dB, is the measurement generally used in contexts like assessing environmental noise or occupational noise exposure and hearing damage risk — a context picked up directly in the next lesson.

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