A brief sound's perceived loudness is lower than a sustained sound at the same sound pressure

What it is

Loudness depends not only on sound pressure level but on how long the sound lasts: a sufficiently brief sound (roughly under two or three hundred milliseconds), even at exactly the same sound pressure level as a longer sustained sound, sounds quieter. A sound has to persist past a certain duration before its perceived loudness reaches the full level that its sound pressure level would otherwise produce; below that duration, the shorter the sound, the bigger the discount on perceived loudness.

It is easy to oversimplify this as "loudness is determined by sound pressure alone." In fact loudness is the joint result of sound pressure and duration, with duration acting as an independent variable — the instantaneous sound pressure level number alone is not enough.

Why it happens

Behind this lies a temporal integration process in how the auditory system judges loudness — roughly understood as a sliding window with a fixed time constant (empirically often on the order of one to two hundred milliseconds), within which the system accumulates sound energy before arriving at a final loudness judgment. If a sound's duration is shorter than this window, the judgment gets "cut off" before energy has fully accumulated, so the resulting loudness is naturally lower than the full loudness that sound pressure level alone would predict. Once duration exceeds this window, further lengthening no longer increases loudness, because the energy accumulable within the window has already reached its ceiling.

This also implies a compensating relationship between sound pressure level and duration within this window: halving a sound's duration roughly requires raising its sound pressure level by some corresponding amount to keep perceived loudness unchanged, up to the window's upper limit.

Studying it

A common method holds sound pressure level fixed while systematically varying a brief tone's duration, measuring how listeners' reported loudness (or detection threshold) changes with duration, then working backward to estimate the rough time constant of the integration window. Some research specifically compares time constants obtained under different measurement criteria — the window estimated from detection-threshold experiments does not exactly match the one estimated from loudness-matching (supra-threshold loudness judgment) experiments.

This data is commonly cited in setting auditory alarm standards, used to specify the minimum duration for a single note or pulse in an alarm sound, avoiding a sound designed too short and getting "discounted" in actual perception.

Where it stops holding

• Temporal integration only holds below the window's duration; beyond that upper limit, loudness no longer grows with duration and is once again determined purely by sound pressure level.
• The specific time constant varies across studies and across judgment criteria (detection threshold versus loudness matching); no single millisecond figure should be treated as a universally precise value — it should be taken only as an order-of-magnitude reference.
• The size of the effect also varies somewhat with frequency; performance should not be assumed identical across all frequencies.

Applying it

• Brief UI sound effects in interfaces (click sounds, tap feedback, short cue tones, often one to two hundred milliseconds or shorter), if leveled purely by meter reading (a peak meter or an instantaneous loudness meter), can easily end up "reading the same on the meter but sounding weaker than a longer sound effect" — this is a systematic bias caused by the temporal integration effect, not a matter of picky ears.
• When mixing or calibrating such short sound effects, their peak levels need to be set higher than a sustained sound at the equivalent perceived loudness to actually achieve the intended loudness in real listening; exactly how much higher depends on the effect's actual duration and target loudness — there is no single universal compensation value, and it requires repeated calibration by ear.
• How to check: run subjective loudness-matching tests comparing a short sound effect against a sustained sound, having listeners judge whether the two sound equally loud, rather than trusting the numeric reading from a peak or instantaneous loudness meter alone.

Related

• Same group: A3.02.1 Loudness does not scale linearly with sound pressure, so volume controls should step by loudness, not pressure · A3.02.2 Ambient noise sets the usable loudness floor · A3.02.3 Equal-loudness contours curl up at the low and high ends, making bass and treble harder to notice at low volume · A3.02.5 A uniform volume number across devices does not guarantee uniform perceived loudness
• Nearby: A3.13 Temporal resolution and rhythm perception
• Search terms: temporal integration of loudness · loudness summation · short tone loudness · alarm pulse duration