# Acoustics/Fundamentals of Psychoacoustics

![](Acoustics_Psychoacoustics.jpg "Acoustics_Psychoacoustics.jpg")

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.

![](Audible.JPG "Audible.JPG")

## 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.

![](Curve_isofoniche.svg "Curve_isofoniche.svg")

### 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.

```{=html}
<center>
```
![](dba.JPG "dba.JPG")

```{=html}
</center>
```
*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.

