What Causes the Initial Acceleration Phase in Molecular Behavior?

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Discussion Overview

The discussion centers around the initial acceleration phase in molecular behavior, particularly in the context of sound propagation and molecular motion in air. Participants explore how the movement of air molecules relates to the speed of sound and the effects of a dropped object on molecular acceleration.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question whether molecular movement occurs at the speed of light and how this relates to sound propagation.
  • Others clarify that sound propagates at the speed of sound, not instantaneously, and that air molecules can be moving slower than this speed.
  • There is a suggestion that the energy from a dropped stone can create an audible sound, raising questions about the sensitivity of human hearing.
  • Some participants assert that air molecules are already moving faster than the speed of sound due to thermal motion, which is distinct from sound propagation.
  • A reference to Feynman's lecture is made, discussing the relationship between sound speed and root mean square velocity of molecules.

Areas of Agreement / Disagreement

Participants express differing views on the nature of molecular motion and sound propagation, with no consensus reached on the initial acceleration phase or the implications of thermal motion.

Contextual Notes

The discussion includes references to the speed of sound, thermal velocity, and mean free path, but lacks clarity on specific assumptions and definitions related to these concepts.

ndvcxk123
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Princeton U. has a great intro to molec. behav. w. sound, but neither there or elsewhere have I found much on the initial acceleration phase. Is it assumed that movement over these nano-distances is already happening at c - and then there is just more of it ? How can a little stone you drop on a table from 3 cm cause this acceleration among the molecules so that it reaches an observer instantly at some distance?
 
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Sorry, what are you asking ?
 
First of all, it doesn't reach an observer "instantly", it propagates at the speed of sound. Second the speed of sound is the speed of the disturbance. The air molecules can be moving slower than that. Think of shaking a stretched rope to get a wave to propagate down the rope. The individual parts of the rope don't move very far, but the wave can propagate a long distance.
 
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ndvcxk123 said:
Is it assumed that movement over these nano-distances is already happening at c
No. It happens at the speed of sound in air.

ndvcxk123 said:
How can a little stone you drop on a table from 3 cm cause this acceleration among the molecules so that it reaches an observer instantly at some distance?
Again, it happens at the speed of sound in air.
 
ndvcxk123 said:
Is it assumed that movement over these nano-distances is already happening at c - and then there is just more of it ?
The air molecules are already moving faster than the speed of sound, just through standard thermal motion. The speed of sound is slower than the pre-existing thermal motion.
 
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ndvcxk123 said:
How can a little stone you drop on a table from 3 cm cause this acceleration among the molecules so that it reaches an observer instantly at some distance?
Are you asking how the energy of a dropped stone is enough to create an audible sound? Our ears are very sensitive!
 
Look it up on Wikipedia https://en.wikipedia.org/wiki/Thermal_velocity

The key word is mean.

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Now compare that to the speed of sound at sea level and 20 C ... 343 m/s.

Edit: Don't forget that the mean free path is of the order of 100 nm. Pretty short. So do not imagine the molecules traveling like a wind.
 
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Dale said:
The air molecules are already moving faster than the speed of sound
Yes. See Feynman lecture 42 where he shows $$|v_{sound}| \approx \frac {v_{rms}} {\sqrt 3 } $$ It surprises me
 
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