Sense of sound
The ear distinguishes strength, height and color of the sound. The strength of the sound depends on the pressure level. The height of the tone depends on the frequency of the sound. For linear spectrum, the basic (main) harmonic is important.
The musical tone can be high or low, depending on the frequency. The chord can be harmonious (small numbers) and disharmonic (large whole numbers). The color of the sound is determined by the envelope of the linear spectrum. The ear is insensitive on the phase difference between the sound components. In case of noise with continuous spectrum, there is no height of the sound, but there is a color determined by the envelope.
The basic elements of the music are:
>> Melody: the change of the height of the tone;
>> Dynamics: the change of the strength of the sound;
>> Rhythm: successive emphasis.
The characteristics of the sound connected with its movement are: the direction from which sound comes, reverberation and echo.
Hearing aid - Ear
The human organ for hearing, the ear, consists of 3 parts: external, middle and inner ear.
The external ear consists of ear shell and hearing channel. The hearing channel (0.4 cm^2 x 2.5 cm) ends with a sloping membrane (0.8 cm^2). It has good adjustment at 1 kHz. The external ear is turning the acoustics into mechanical oscillations.
The middle ear consists of bones: hammer, anvil and an uplift. It is a mechanical connection between the membrane and the inner ear (transformer). It also protects from excessive sound.
The inner ear has snail body (Kohlea). It's 32 mm long, folded 2.5 times. It consists of window, basilar membrane, lymph, and Corti's organ. For different frequencies the displacement of the basilar membrane is the biggest at different distances from its beginning. On the Corti's organ there are 2350 cells with fibers which end up in nerve fibers as a connection with the brain. The fibers bend and they generating electrical pulses (with maximum frequency of 500 Hz). The connection between the sound and the generated pulses is complex function which is decoded by the brain, in order to create an image for the sound. The both human ears are physiologically independent one from another.
Height of the sound
The height of the sound is determined by its frequency, or by the frequency of the basic harmonic in case of a complex sound. Even when the sound has no basic harmonic, the ear can determine its correct height. The ear listens logarithmic: height of the sound ~ log f.
The hearing range of the ear is from 20 Hz up to 20 kHz. This range covers 10 octaves (16, 31.5, 63, 125, 500, 1k, 2k, 4k, 8k, 16k). One octave has 12 half-tones at musical scale. The difference between two adjacent half-tones is 6%. The ear can determine even less change in the height of the sound. Up to 500 Hz it determines 3 Hz, and above the 500 Hz the difference in determination is df/f = 0.3 %. The ear determines 850 different heights of sound in the whole frequency range. There are 850 places on the basilar membrane with maximal response. These places are displaced from each other at 37 um.
Audible area of the ear
The audible area of the ear is determined by the borders of the strength of the sound. The lower limit or border, it's also known as a hearing threshold. For frequency of 1000 Hz, the pressure is 2 x 10^-5 Pa. The displacement of the molecules is 10^-9 cm. The upper limit is 120 dB and is known as a pain limit:
20log(pmax/p0) = 20log(10^6) = 120 dB
Level of sound
The level of sound in dB has the same value for the pressure and for the sound intensity:
L[dB] = 2log(p/p0)
L[dB] = 2log(J/J0)
J0 = 10^-12 W/m^2 = 10^-6 W/cm^2
p0 = 400 kg/cm^2
The dB unit is good and appropriate because the subjective strength of sound is logarithmic function of pressure (Weber-Fechner law). The sensitivity of the ear is 1 dB.
Subjective strength of sound
The strength of sound expressed in phon:
A[phon] = 20log(p/p0) = 20log(J/J0) at 1 kHz;
The level of sound in dB is equal to the strength of sound in phon for f = 1 kHz. For all other frequencies they are different.
Some examples of the various strengths of sound:
>> Very loud:
- aircraft engine at 3 meters distance - strength of sound: 120 phon;
- compressor at 2 meters distance - strength of sound: 110 phon;
- motor without exhaust at 10 meters distance - strength of sound: 100 phon;
>> Loud:
- a car horn at 5 meters distance - strength of sound: 90 phon;
- strong shouting - strength of sound: 80 phon;
>> Normal:
- urban traffic - strength of sound: 70 phon;
- office - strength of sound: 60 phon;
- normal speech - strength of sound: 50 phon;
>> Calmly:
- silent speech or music - strength of sound: 40 phon;
- quiet apartment - strength of sound: 30 phon;
- peaceful garden - strength of sound: 20 phon;
- leafing - strength of sound: 10 phon;
Sound Volume
The phon scale doesn't show the right way of how the ear determines the subjective strength of sound. The volume is better unit for subjective strength of sound. The unit meter for volume is "sone".
S[sone] = 2^(0.1*(A - 40)), where A is expressed in phon;
It is arbitrarily selected that: 1 Sone = 40 Phon. The Sone scale is experimentally confirmed.