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 \(\text{20 }\micro\text{Pa}\), 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\(\degree\)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, \(I=\int\limits_0^T p(t)v(t)dt\). For a plane wave, this is \(I=2\pi^2v^2A^2\).
• Neper
• Richter Scale
• pH scale

Units of frequency level

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