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Non-linear hearing

For the normal average organ of hearing of a person, there are some limit (threshold) minimum values ​​of the physical parameters of the sound field, at which there is still an auditory sensation. Such a threshold of audibility is the standardized sound intensity I0 = 10 … 12 W / m2 (close to the threshold of audibility at f = 1000 Hz in silence), as well as the corresponding sound pressure p0 = 2 * 10-5 Pa and sound energy density e03 * 10-15 J / m3. The hearing threshold is private dependent. Above the threshold of hearing is the hearing area. In fig. 1 shows a curve of the threshold of audibility. The upper threshold of audibility is also shown there, above which the destruction of the organ of hearing can occur – the pain threshold, which corresponds to pressure pmax = 150 … 200 Pa, which exceeds 107 times p0 = 2 * 10-5 Pa.

About non-linear hearing (Non-linear hearing)
Fig. 1. Curves that limit hearing

For more convenient handling of such significant absolute values, but to a greater extent because the auditory sensation of the annoying power of the sound signal is proportional to its logarithm (according to Weber-Fechner law), values ​​called sound intensity level (LI), sensation level (E) are more often used , sound pressure level (LP), sound energy density level (LE), which are also proportional to the logarithm of the relative value of the parameter (I / I0), (p / p0), (e / e0) and are measured in decibels:

On non-linear hearing (Non-linear hearing) (1.1)

On non-linear hearing (Non-linear hearing) (1.2)

On non-linear hearing (Non-linear hearing) (1.3)

The same relative changes in irritating power cause the same increment in auditory sensation. This hearing feature is also measured: the threshold for detecting changes in the intensity (DI) of pure tones at high and medium levels of sensation E is from 0.2 to 0.6 dB, at low levels of sensation it reaches a few decibels, and the average DI / I is about 1 dB Thus, between the threshold of audibility and the pain threshold, hearing distinguishes several hundred degrees of change in auditory sensation.

The amplitude resolution of hearing in terms of sensing changes in sound intensity also has a frequency dependence: it is highest at medium, noticeably lower at high and even lower at low frequencies.

It was found that the volume level inaccurately characterizes the subjective auditory sensation. To overcome this, the concept of volume level (LG) was introduced. For the LG volume level of a given sound, the intensity level of a pure tone equally loud with it is taken at a frequency of 1000 Hz. The unit of measure LG is the background. In binaural listening (i.e., with both ears) of pure tones, the isophone family is used to determine the volume level, i.e. curves of equal volume (Fig. 2).

About non-linear hearing (Non-linear hearing)
Fig. 2. Equal volume curves of sinusoidal sounds

Sometimes isofone graphs cause some difficulties in perceiving their essence. To simplify understanding, a more accessible graph is presented (Fig. 3), which characterizes the sensitivity of hearing at various volume levels. The unit of volume is 1 dream, corresponding to the volume of the tone with the level LG = 40 background.

About non-linear hearing (Non-linear hearing)
Fig. 3. Frequency characteristics of hearing sensitivity at various volume levels

Table 1 shows the measured values ​​of the LG volume level and G volume for some sound sources and the gradation of volume in music programs.

Sound source LG, background G, sleep Street with heavy traffic and a tram 75 … 80 11.40 … 17.10 Noisy street without a tram 60 … 75 4.35 … 11.40 Normal average noise on the street 55 … 60 3.08. ..4.35 The room is noisy 40 … 50 0.98 … 2.20 The room is quiet 25 … 30 0.20 … 0.36 The conversation of three people in the room 45 … 50 1.50 … 2.20 Orchestra 80 … 100 17.10. ..88.00 Hall for mass scenes 75 … 90 11.40 … 59.00 Applause 60 … 75 4.35 … 11.40 Solo in the studio 40 … 50 0.98 … 2.20 Forte fortissimo 100 88.00 Fortissimo 90 38.00 Forte 80 17.10 Mezzo-forte 70 7.95 Mezzo piano 60 4.35 Piano 50 2.20 Pianissimo 40 0.98 Piano pianissimo 30 0.36 Threshold of auditory sensation 0 0

Table 1.

A person’s hearing aid is not able to feel the effects of sounds in a significant range of intensities in a completely linear fashion. Non-linearity of hearing is manifested in the fact that when exposed to loud tones with an intensity level of more than 40 dB, for example, with a frequency of f1, harmonics of this tone with frequencies of 2f1, 3f1, 4f1, etc. At a sound intensity level of less than 40 dB, subjective harmonics are not formed. The optimal level at which the visibility and serial number of the harmonic is relatively small, can be considered 80 … 90 dB. The 7th and 9th harmonics are especially dissonant. The 2nd subjective harmonic is almost 5 times superior to the 3rd. This fact is sometimes the basis for the assertion that SE amplifiers, in which the objective 2nd harmonic usually already predominates, are more appealing to the hearing than PP amplifiers, where the 3rd objective harmonic dominates.

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