Undergrad What Causes the Initial Acceleration Phase in Molecular Behavior?

[ndvcxk123]

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?

 

[hmmm27]

Sorry, what are you asking ?

 

[phyzguy]

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.

 

[DaveC426913]

Is it assumed that movement over these nano-distances is already happening at c

No. It happens at the speed of sound in air.

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.

 

[Dale]

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.

 

[russ_watters]

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!

 

[anorlunda]

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.

 

[hutchphd]

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