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Like the decibel, the neper is a unit in a logarithmic scale. While the bel uses the decadic (base-10) logarithm to compute ratios, the neper uses the natural logarithm, based on Euler's number (e ≈ 2.71828). The level of a ratio of two signal amplitudes or root-power quantities, with the unit neper, is given by [2]
E is the sound exposure; E 0 is the reference sound exposure; 1 Np = 1 is the neper; 1 B = 1 / 2 ln 10 is the bel; 1 dB = 1 / 20 ln 10 is the decibel. The commonly used reference sound exposure in air is [2] = .
The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. Until the mid-1920s, the unit for loss was miles of standard cable (MSC). 1 MSC corresponded to the loss of power over one mile (approximately 1.6 km) of standard telephone cable at a frequency of 5000 radians per second (795.8 Hz), and matched closely the smallest attenuation detectable to a ...
Examples of logarithmic units include units of information and information entropy (nat, shannon, ban) and of signal level (decibel, bel, neper). Frequency levels or logarithmic frequency quantities have various units are used in electronics ( decade , octave ) and for music pitch intervals ( octave , semitone , cent , etc.).
The neper, bel, and decibel (one tenth of a bel) are units of level that are often applied to such quantities as power, intensity, or gain. [6] The neper, bel, and decibel are related by [7] 1 B = 1 / 2 log e 10 Np; 1 dB = 0.1 B = 1 / 20 log e 10 Np
Sound power or acoustic power is the rate at which sound energy is emitted, reflected, transmitted or received, per unit time. [1] It is defined [2] as "through a surface, the product of the sound pressure, and the component of the particle velocity, at a point on the surface in the direction normal to the surface, integrated over that surface."
While 1 atm (194 dB peak or 191 dB SPL) [11] [12] is the largest pressure variation an undistorted sound wave can have in Earth's atmosphere (i. e., if the thermodynamic properties of the air are disregarded; in reality, the sound waves become progressively non-linear starting over 150 dB), larger sound waves can be present in other atmospheres ...
A sound with a loudness of 1 sone is judged equally loud as a 1 kHz tone with a sound pressure level of 40 decibels above 20 micropascals. [1] The phon is psychophysically matched to a reference frequency of 1 kHz. [2] In other words, the phon matches the sound pressure level in decibels of a similarly perceived 1 kHz pure tone. [3]