Logarithmic Scale

It is a scale where values are plotted by their logarithmic values. This is commonly used to display values with a large variation in data, such as exponential growths. A logarithmic graph is non-linear.

Units of information

• Bit, Byte
• Harley / Ban / Dit
• Nat / Nit / Nepit
• Shannon

Units of level

• Decibel, Bel
  • For sound in air, the decibel scale measures the sound pressure level (SPL) relative to an air pressure of $\text{20 }\text{micro}\text{Pa}$, which is approximately the sound of a mosquito flying 3 metres away, which is considered the threshold of human hearing.
  • Sound Intensity Level (SIL) is different, and varies according to the room conditions. The human auditory threshold has an SIL of 0.98 $pW/m^2$ at 1 atm and 25$°$C.
  • SIL can be related to SPL by the specific acoustic impedance value ${\text{z}}_0$, At ambient temperature, ${\text{z}}_0$ = 410 Pa-s/m, and therefore the reference value ${\text{I}}_0$ = 1 $pW/m^2$.
  • I=pv, where p is the pressure and v is the velocity.
    • For a given period, $I=\underset{0}{\overset{T}{\int }}p(t)v(t)dt$. For a plane wave, this is $I=2{\pi }^2{v}^2{A}^2$.
• Neper
• Richter Scale
• pH scale

Units of frequency level

• Decade, decidecade, savart (10 times apart)
• Octave, tone, semitone, cent