Motion of Volumes of Air in a Wave-Filled Tube

[Shatzkinator]

Homework Statement

Imagine a row of many small volumes of air (each consisting of many billions of molecules) along the entire length of a tube that is open at one end. Describe the motion of these small volumes of air when the standing wave, represented by Fig2 (sound wave in a closed tube), is produced. Which of the small volumes of air along the tube move fastest/slowest? What is the direction of motion (along the tube or perpendicular to it)?

Homework Equations

none

The Attempt at a Solution

The volumes of air at the highest wave amplitude will move the fastest. The molecules will vibrate parallel to the direction of the wave.

Is this correct? Thanks for any input.

 

[anathema]

I would like to clarify a few points about the motion of the small volumes of air in this scenario. First of all, the motion of the air molecules is not solely determined by the amplitude of the wave, but also by the frequency and wavelength of the wave. The faster the frequency and shorter the wavelength, the faster the molecules will vibrate.

In a standing wave, the molecules at the nodes (points of zero amplitude) will have the slowest motion, while the molecules at the antinodes (points of maximum amplitude) will have the fastest motion. This is because at the nodes, the molecules are not experiencing any displacement and therefore do not vibrate, while at the antinodes, the molecules are experiencing maximum displacement and therefore vibrate the most.

The direction of motion for the air molecules will be perpendicular to the direction of the wave. This is because the wave is a longitudinal wave, meaning the molecules are vibrating back and forth in the same direction that the wave is traveling. Therefore, the motion of the molecules is perpendicular to the direction of the tube, which is also the direction of the wave.

I hope this helps to clarify the motion of the small volumes of air in a standing wave scenario.

 

[nlightner]

Yes, your answer is correct. When a standing wave is produced in a tube, the air molecules will vibrate back and forth in the same direction as the wave. The volumes of air at the nodes (points of zero displacement) will experience the least movement, while the volumes of air at the antinodes (points of maximum displacement) will experience the greatest movement. This is because the antinodes have the highest amplitude of the standing wave. So, the volumes of air at the antinodes will move the fastest, while the volumes of air at the nodes will move the slowest. Their motion will be parallel to the direction of the wave, along the length of the tube.