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The most direct physical correlate of loudness is sound intensity (or sound pressure) measured close to the eardrum. However, many other factors also influence the loudness of a sound, including its frequency content, its duration, and the context in which it is presented. Some of the earliest psychophysical studies of auditory perception, going back more than a century, were aimed at examining the relationships between perceived loudness, the physical sound intensity, and the just-noticeable differences in loudness (Fechner, 1860; Stevens, 1957).

The loudness of a given sound is closely associated with the amplitude of the sound wave. Higher amplitudes are associated with louder sounds. Loudness is measured in terms of decibels (dB), a logarithmic unit of sound intensity. A typical conversation would correlate with 60 dB; a rock concert might check in at 120 dB. A whisper 5 feet away or rustling leaves are at the low end of our hearing range; sounds like a window air conditioner, a normal conversation, and even heavy traffic or a vacuum cleaner are within a tolerable range. However, there is the potential for hearing damage from about 80 dB to 130 dB: These are sounds of a food processor, power lawnmower, heavy truck (25 feet away), subway train (20 feet away), live rock music, and a jackhammer. The threshold for pain is about 130 dB—a jet plane taking off or a revolver firing at close range (Dunkle, 1982).

The decibel (dB) quantifies sound pressure level (SPL). A decibel is a relative measure—a loudness relative to another loudness. To calculate Sound Pressure Level, we use a reference sound intensity of 20 micropascals. It is very useful to remember that an increase in SPL of 20dB represents a 10-fold increase in the amplitude of the pressure wave.

SPL= 20log(P/P₀) =10log(P²/P²₀) = 10log(I/I₀)

Decibels are calculated by the following equation: SPL= 20log(P/P₀). Intensity is the square of the pressure. Intensity is power. So another way of writing the equation above is SPL=10log(P²/P²₀) = 10log(I/I₀). Note: A decibel is 10 bels; a bel is log(I/I₀). A 20Pa (120dB) sound is about 1 Watt of energy.

Perception of loudness vs. stimulus intensity is a compressive function. The use of a logarithmic function (decibels) to characterize sound pressure level makes it a little hard to see. If you plot perceived loudness against dB, you get a function that is essentially linear, maybe even scooping up a bit. However, when you plot perceived loudness against the amplitude of the pressure wave, or even against intensity (pressure squared), you see that our perception of loudness is compressive: the louder a sound is, the bigger the change needs to be before we notice it. The Active Learning Exercise at the end of this chapter lets you do a magnitude estimation experiment to discover your own psychometric function for describing your perception of loudness as a function of sound pressure level (although the speakers on our devices often have some non-linearities, so we’d have to use carefully calibrated equipment to get an exact answer).