Loudness is the perceptual experience associated with the strength of an auditory stimulus, and it is influenced strongly by the sound pressure level reaching the ear. Sound pressure is the small variation in pressure produced by a sound wave, while sound intensity represents acoustic power transmitted per unit area. Sound pressure level is normally expressed in decibels relative to a reference pressure, with the standard reference for air acoustics being 20 micropascals.
Because human hearing covers an enormous range of sound pressures, a logarithmic decibel scale is used rather than a simple linear scale. Loudness, however, is not identical to sound pressure level. It is a perceptual quantity influenced by frequency, duration, waveform, bandwidth, the listener's hearing sensitivity and the acoustic environment. Two sounds with identical measured sound pressure levels can therefore be perceived as having different loudness.
Sound intensity and sound pressure level are related but should not be treated as interchangeable concepts. For a plane progressive sound wave under appropriate conditions, intensity is related to the square of root mean square sound pressure divided by the product of medium density and sound speed. Sound intensity level uses a reference intensity, while sound pressure level uses a reference pressure.
In practical environmental and occupational acoustics, sound pressure level is commonly measured with sound level meters because it can be measured at a location without directly determining total acoustic power. Acoustic power describes the rate at which a source emits sound energy, whereas sound pressure level describes the resulting pressure fluctuation at a measurement position. The measured level therefore depends on source strength, distance, room characteristics and propagation conditions.
The decibel scale is logarithmic. An increase of 10 decibels corresponds to a tenfold increase in intensity under the relevant reference conditions, while an increase of approximately 3 decibels corresponds to roughly a doubling of intensity. Sound pressure level uses twenty times the base ten logarithm of the ratio between measured root mean square pressure and reference pressure. Because pressure is an amplitude quantity whereas intensity is proportional to pressure squared, the numerical formulas differ.
A 20 decibel increase in sound pressure level corresponds to a tenfold increase in pressure amplitude under the same conditions. The logarithmic scale allows very large physical ranges to be represented with manageable numbers, but decibel values should not be interpreted as though a difference of 10 decibels always means ten times as loud perceptually.
Human loudness perception depends strongly on frequency. The ear is not equally sensitive to all audible frequencies, and sensitivity is generally greatest over a broad middle frequency range important for human speech. At low sound levels, the threshold of hearing varies substantially with frequency, so a low frequency tone may need a considerably higher sound pressure level than a mid frequency tone to be perceived.
Equal loudness contours describe the sound pressure levels required at different frequencies to produce approximately equal perceived loudness for a reference tone. These contours demonstrate why sound level meters sometimes apply frequency weightings. A weighting such as A weighting approximates aspects of human hearing sensitivity under particular measurement conditions, while C weighting provides a flatter response and is more sensitive to low frequency energy.
Duration and temporal structure also influence loudness. A sound that lasts only briefly can be perceived differently from a sustained sound of the same instantaneous level. The auditory system integrates acoustic information over time, although the exact relationship is complex and depends on duration, frequency and sound structure. Sounds with rapidly changing amplitude can produce different percepts from steady sounds with the same average energy.
The distinction between peak level, maximum level, equivalent continuous level and other acoustic metrics is therefore important in practical measurement. Occupational noise assessment, environmental noise assessment and audio engineering use different quantities depending on whether the concern is average exposure, transient peaks, perceptual loudness or equipment limits.
Distance from a sound source affects the sound pressure level received by an observer. For an ideal point source radiating uniformly in a free field, acoustic intensity decreases approximately with the inverse square of distance, producing a decrease of about 6 decibels for each doubling of distance. Real environments are more complicated because sound can reflect, absorb, scatter and diffract. Indoors, reverberation can maintain sound energy after direct sound has weakened, while barriers can reduce transmission through shadowing and diffraction. Atmospheric absorption becomes increasingly important at higher frequencies over long distances. These environmental factors mean that loudness at a listener is determined not only by the source but also by the complete acoustic pathway between source and receiver.
Loudness is also affected by the spectral composition of a sound. A complex sound containing multiple frequency components can have a different perceived loudness from a pure tone at the same nominal sound pressure level. Masking occurs when one sound reduces the audibility or perceptual prominence of another, with particularly strong effects when frequencies are close or when one sound has substantially greater energy.
The auditory system processes sounds through frequency selective channels, and interactions among these channels contribute to loudness perception. Psychoacoustic models attempt to predict perceived loudness from physical sound parameters, but no single physical measurement fully captures all aspects of subjective loudness. Individual differences in hearing thresholds and auditory health also affect perception.
Loudness should therefore be distinguished from acoustic amplitude, sound pressure, sound intensity, sound power and decibel level. These physical quantities are related but represent different properties. Loudness is a perceptual attribute constructed by the auditory system. Sound pressure level is a measurable acoustic quantity. A high sound pressure level can damage hearing, particularly with sufficient exposure duration, even if the sound is not perceived as extremely loud because of frequency characteristics or hearing impairment.
Conversely, a sound can be perceived as relatively loud without having an unusually high total acoustic power if its frequency content lies in a highly sensitive region of hearing. Understanding loudness therefore requires combining physical acoustics with psychoacoustics and exposure science rather than treating a decibel value as a direct measurement of subjective loudness.
