# Acoustics/Fundamentals of Psychoacoustics

Due to the famous principle enounced by Gustav Theodor Fechner, the sensation of perception doesn’t follow a linear law, but a logarithmic one. The perception of the intensity of light, or the sensation of weight, follow this law, as well. This observation legitimates the use of logarithmic scales in the field of acoustics. A 80 dB (10-4 W/m²) sound seems to be twice as loud as a 70 dB (10-5 W/m²) sound, although there is a factor 10 between the two acoustic powers. This is quite a naïve law, but it led to a new way of thinking about acoustics: trying to describe the auditive sensations. That’s the aim of psychoacoustics. As the neurophysiological mechanisms of human hearing haven’t been successfully modeled, the only way of dealing with psychoacoustics is by finding metrics that best describe the different aspects of sound.

## Perception of sound

The study of sound perception is limited by the complexity of the human ear mechanisms. The figure below represents the domain of perception and the thresholds of pain and listening. The pain threshold is not frequency-dependent (around 120 dB in the audible bandwidth). At the opposite side, the listening threshold, as all the equal loudness curves, is frequency-dependent. In the center are typical frequency and loudness ranges for human voice and music.

## Phons and sones
### Phons

Two sounds of equal intensity do not have the same apparent loudness, because of the frequency sensibility of the human ear. An 80 dB tone at 100 Hz does not sound as loud as an 80 dB tone at 3 kHz. A new unit, the phon, is used to describe the loudness of a harmonic sound. X phons means “as loud as X dB at 1000 Hz”. Another tool is used : the equal loudness curves, a.k.a. Fletcher curves.

### Sones

Another scale currently used is the sone, based upon the rule of thumb for loudness. This rule states that the sound must be increased in intensity by a factor 10 to be perceived as twice as loud. In decibel (or phon) scale, it corresponds to a 10 dB (or phons) increase. The sone scale’s purpose is to translate those scales into a linear one.
$\log(S)=0,03(L_{ph}-40)$
Where S is the sone level, and $L_{ph}$ the phon level. The conversion table is as follows:
| Phons | Sones |
| 100 | 64 |
| 90 | 32 |
| 80 | 16 |
| 70 | 8 |
| 60 | 4 |
| 50 | 2 |
| 40 | 1 |

## Metrics

We will now present five psychoacoustics parameters to provide a way to predict the subjective human sensation.

### dB A

The measurement of noise perception with the sone or phon scale is not easy. A widely used measurement method is a weighting of the sound pressure level, according to frequency repartition. For each frequency of the density spectrum, a level correction is made. Different kinds of weightings (dB A, dB B, dB C) exist in order to approximate the human ear at different sound intensities, but the most commonly used is the dB A filter. Its curve is made to match the ear equal loudness curve for 40 phons, and as a consequence it’s a good approximation of the phon scale.
Example : for a harmonic 40 dB sound, at 200 Hz, the correction is -10 dB, so this sound is 30 dB A.

### Loudness

It measures the sound strength. Loudness can be measured in sone, and is a dominant metric in psychoacoustics.

### Tonality

As the human ear is very sensible to the pure harmonic sounds, this metric is a very important one. It measures the number of pure tones in the noise spectrum. A broadwidth sound has a very low tonality, for example.

### Roughness

It describes the human perception of temporal variations of sounds. This metric is measured in asper.

### Sharpness

Sharpness is linked to the spectral characteristics of the sound. A high-frequency signal has a high value of sharpness. This metric is measured in acum.

### Blocking effect

A sinusoidal sound can be masked by a white noise in a narrowing bandwidth. A white noise is a random signal with a flat power spectral density. In other words, the signal's power spectral density has equal power in any band, at any centre frequency, having a given bandwidth. If the intensity of the white noise is high enough, the sinusoidal sound will not be heard. For example, in a noisy environment (in the street, in a workshop), a great effort has to be made in order to distinguish someone’s talking.
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