Mean free path: Difference between revisions

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In molecular physics, mean free path is the mean distance a molecule, atom, or other gas unit can travel before collision with other particles.

In molecular physics, '''mean free path''' is the mean distance a molecule, atom, or other gas unit can travel before collision with other particles. It determines the largest frequency that can possibly propagate in a gas. Any larger frequencies will not propagate, owing to the fact that molecules will not transfer the pressure wave.

It is defined by

In air at <abbr title="Standard temperature and pressure ">STP</abbr>, mean free path is about 68 nm. Together with the sound speed of 340 m/s, the maximum physically possible frequency is about 5 GHz.

== Definition ==

Mean free path is defined by

:<math>\ell = \frac{\mu}{p} \sqrt{\frac{\pi k_\text{B} T}{2 m}},</math>

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where:

<math>\ell</math> is the mean free path,

: <math>\ell</math> is the mean free path,

<math>m</math> is the mass of the particle

: <math>m</math> is the mass of the particle,

<math>M</math> is the molar mass of the substance

: <math>M</math> is the molar mass of the substance,

<math>\mu</math> is the gas's viscosity

: <math>\mu</math> is the gas's viscosity,

<math>R</math> is the universal gas constant

: <math>R</math> is the universal gas constant,

Kb is Boltzmann constant,

: k<sub>B</sub> is the Boltzmann constant,

T is temperature

: T is the temperature,

P is ~~pressure~~

: P is the pressure.

~~== Application ==~~

~~Mean free path determines the largest frequency that can possibly propagate in a gas. Any larger frequencies will not propagate, owing to the fact that molecules will not transfer~~ the pressure ~~wave~~.

~~In air at <abbr title~~=~~"Standard temperature and pressure ">STP</abbr>, mean free path is about 68 nm. Together~~ with ~~340 m/s sound speed, this gives a maximum of 5 GHz of frequency.~~ If there is a species which can hear this high of a sound, the maximum ~~EDO~~ which can be applied will be defined by the species' lowest frequency, or the place where the difference between rhythm and pitch occurs.

== Analysis with respect to equal-step tunings ==

If there is a species which can hear this high of a sound, the maximum edo which can be applied will be defined by the species' lowest frequency, or the place where the difference between rhythm and pitch occurs.

If the beat rate is less than the lowest frequency,beats are distinct, and the interval sounds like a "wahwah" instead of a true sound pair.

@@ Line 1: / Line 1: @@
 {{Wikipedia|Mean free path}}
-In molecular physics, mean free path is the mean distance a molecule, atom, or other gas unit can travel before collision with other particles.
+In molecular physics, '''mean free path''' is the mean distance a molecule, atom, or other gas unit can travel before collision with other particles. It determines the largest frequency that can possibly propagate in a gas. Any larger frequencies will not propagate, owing to the fact that molecules will not transfer the pressure wave.
-It is defined by
+In air at <abbr title="Standard temperature and pressure ">STP</abbr>, mean free path is about 68 nm. Together with the sound speed of 340 m/s, the maximum physically possible frequency is about 5 GHz.
+== Definition ==
+Mean free path is defined by
 :<math>\ell = \frac{\mu}{p} \sqrt{\frac{\pi k_\text{B} T}{2 m}},</math>
@@ Line 12: / Line 15: @@
 where:
-<math>\ell</math> is the mean free path,
+: <math>\ell</math> is the mean free path,
-<math>m</math> is the mass of the particle
+: <math>m</math> is the mass of the particle,
-<math>M</math> is the molar mass of the substance
+: <math>M</math> is the molar mass of the substance,
-<math>\mu</math> is the gas's viscosity
+: <math>\mu</math> is the gas's viscosity,
-<math>R</math> is the universal gas constant
+: <math>R</math> is the universal gas constant,
-Kb is Boltzmann constant,
+: k<sub>B</sub> is the Boltzmann constant,
-T is temperature
+: T is the temperature,
-P is pressure
+: P is the pressure.
-== Application ==
-Mean free path determines the largest frequency that can possibly propagate in a gas. Any larger frequencies will not propagate, owing to the fact that molecules will not transfer the pressure wave.
-In air at <abbr title="Standard temperature and pressure ">STP</abbr>, mean free path is about 68 nm. Together with 340 m/s sound speed, this gives a maximum of 5 GHz of frequency. If there is a species which can hear this high of a sound, the maximum EDO which can be applied will be defined by the species' lowest frequency, or the place where the difference between rhythm and pitch occurs.
+== Analysis with respect to equal-step tunings ==
+If there is a species which can hear this high of a sound, the maximum edo which can be applied will be defined by the species' lowest frequency, or the place where the difference between rhythm and pitch occurs.
 If the beat rate is less than the lowest frequency,beats are distinct, and the interval sounds like a "wahwah" instead of a true sound pair.