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Psychoacoustics
Psychoacoustics is a branch of a broader science called psychophysics, which many consider to be psychology's gateway to science. To understand this field, it is important to make the distinction between a physical and a perceptual measure. For example, while waiting in line for 15 minutes at the post office, one might think: “This is taking a lot of time; it feels like I have been waiting for hours,” one is making the distinction between a physical measure (15 minutes) and a perceptual measure (hours). Psychophysics is the science that studies the relationship between those two measures.
Psychoacoustics is specifically interested in the relationship between an acoustic phenomena and the auditory perception that it generates. Airborne vibration is picked up by the listener through his auditory system, and is eventually translated into an auditory sensation. Psychoacoustic experiments attempt to quantify these sensations through asking a listener questions designed to determine the influence of variation of a physical parameter on auditory perception. A simple acoustic wave produced by a pure tone can be described mathematically as:

Where s(t) is the pressure at the time t, A is the maximum amplitude, f the frequency of the sound, and τ is the phase. As the frequency (physical measure) of the sound is increased, the listener will perceive the sound as increasing in pitch (perceptual measure). As the amplitude (physical measure) of the sound is increased, the listener will perceive the sound as increasing in loudness (perceptual measure). If the sound pressure was measured at the entry of both ear canals of a listener, the difference of amplitude and phase between the two physical measures will indicate how the listener will localize the sound source. Furthermore, if the sound was composed of many harmonics, the relationship between the amplitude of each harmonic (the spectral envelope) will influence the perception of timbre. Table 1 summarizes the different physical parameters of a sound and their perceptual correlates. These relationships are considered “primary” because each physical parameter will mainly influence its associated sensation. A physical parameter can also have a “secondary” effect on other sensations. For example, the frequency will have also an effect on the loudness of a sound: At equal amplitude, a 100 Hz tone will be perceived as much softer than a 2,000 Hz tone.
| Table 1 The physical parameters of a sound and their perceptual correlates | |
|---|---|
| Physical Parameter | Sensation |
| Frequency | Pitch |
| Amplitude | Loudness |
| Spectral envelope | Timbre: brightness |
| Temporal envelope | Timbre: impulsiveness |
| Interaural temporal difference | Localization |
| Interaural level difference | |
| Physical duration | Perceptual duration |
Origin of Psychoacoustics and Weber's Law
Previously, great scholars such as Immanuel Kant (1724–1804) thought that since mathematics could not be applied to the soul, psychology was not and would never be a science. However, in 1860, Gustav Fechner (1801–87), a German psychologist, showed otherwise in his book Elemente der Psychophysik (Element of Psychophysics). This book lays the foundation for this new science, which aims to study the relationship between physical stimuli and the sensations tha they induce. It draws on the work of a German physician in the early 19th century, Ernst Weber (1795–1878), and his famous law issued in 1831, which states that the minimum amount of a physical parameter increase δφ needed to induce a perceptible change between two stimuli is proportional to the magnitude, φ, of the stimuli.
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