If I’m not mistaken, sound travels at about 340m/s at 20 °C 1 atmosphere. This would happen due to longitudinal waves caused by collisions between air particles.
From my calculations I concluded that at those conditions of temperature and pressure, an oxygen molecule moves at 480 m/s and that of nitrogen at 510 m/s.
How can they continue a “chain of collisions” if they are already moving faster than the “chain collision” itself?
Answer
You have to distinguish between the particle speed (this is the speed of a physical particle in the gas) and the wave speed (that is the speed at which the disturbance propagates).
For starters, the particle velocity you calculated is the average velocity of the molecules of an undisturbed medium. This is a chaotic movement of the particles and in itself has nothing to do with a wave. This average velocity of the particles ultimately determines the temperature of the gas and, combined with the number of particles per unit volume, also determines the pressure.
In the case of a sound wave, the air molecules on top of this chaotic movement acquire another reciprocating movement (caused, for example, by a vibrating loudspeaker membrane). That motion is the particle speed of the wave. Its magnitude depends on the intensity of the sound wave, but is in any case much smaller than the average thermal velocity. At the weakest level of intensity that we can hear, the deflection of the molecules from their equilibrium state is barely ten to the minus eleventh meter! That is less than the diameter of an atom. The corresponding particle speed depends on the frequency (how often the particle has to move back and forth per unit time), and at 1000 Hz is on the order of ten to minus eight meters per second.
How fast a disturbance propagates in a gas (speed of sound) does not depend on the magnitude of the deflection of each particle, but on the number of collisions that the particles have with each other per unit time (and this depends on the pressure) and on the mass (inertia) of the particles.
Have a look at the attached applet. If you follow an individual particle, you can see the particle speed of the wave. The speed of the disturbance is shown from left to right.
So the particle speed has nothing to do with the wave speed. For a transverse wave they even have a different direction.
Answered by
Prof Walter Lauriks
Physics Acoustics
Old Market 13 3000 Leuven
https://www.kuleuven.be/
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