neper
Sound levelexact by definition
The neper is the natural-logarithm counterpart of the decibel: a level of one neper is a ratio of e in amplitude, or e² in power. One neper is exactly 20/ln(10) decibels, about 8.6858896381, so the relation between the two is exact by definition even though the number is irrational. It is used for attenuation in transmission lines, waveguides and acoustic media, where working in natural logarithms keeps the exponential decay constant in the equation rather than in a conversion factor.
Watch out: The conversion assumes the ISO 80000 convention, in which a level in nepers is the natural logarithm of a field quantity ratio and half the natural logarithm of a power ratio. That is what makes 1 Np equal 8.6859 dB whether the underlying quantity is amplitude or power. Never add a figure in nepers to one in decibels without converting; the two look interchangeable and are not.
| 1 Np | 8.6858896 dB |
Named for John Napier, who published the first logarithms in 1614. The neper is a coherent unit within the SI system of logarithmic ratio quantities, where the decibel is the one that gets used and the neper is the one that keeps the mathematics clean.