I have been utterly confused as to what exactly happens in a sound wave and how it is produced.I understand the mathematical description of it quite well, what I don't get is its qualitative description.

So suppose I have a long air tube and I create a sound wave travelling right by sinusoidally moving the piston right and left. Now here are my questions:

  1. Doesn't pushing the piston change the volume of the tube and as a result the pressure through out the tube changes? Then how come the pressure vary sinusoidally?
  2. I read a bunch of books but no one book seems to explicitly explain how the sound wave is produced. I have read that pushing the piston compresses the layers of air next it causing the pressure and density to increase there. Then does this region of increased pressure cause the adjacent layers to compress or is the air molecules in this high pressure region push the layers adjacent to them causing them to compress?
  3. If the above description is correct then how come the displacement and pressure equations are out of phase by π/2? I.e how come when the pressure variation at a place is zero then the displacement of air molecules is maximum there?
  4. Can someone provide a qualitative description of how a sound wave is produced by sinusoidally moving the piston in the air tube?
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    $\begingroup$ Doesn't pushing the piston change the volume of the tube and as a result the pressure through out the tube changes? Then how come the pressure vary sinusoidally? The pressure disturbance is the sound wave, so moving the piston doesn't instantaneously change the pressure in the tube from one constant value to another constant value. The change in pressure propagates through the tube at the speed of sound in the tube. $\endgroup$ – Aaron Stevens Mar 27 '19 at 16:40
  • $\begingroup$ I understand that.. $\endgroup$ – Lucifer Mar 27 '19 at 17:04
  • $\begingroup$ Re, "...as a result the pressure through out the tube changes?..." When the piston starts to move, the only air molecules that can "know" that it has started to move are the ones that actually are bumping right up against it. Then their neighbors get the message, then their neighbors, etc. It takes time for the information to travel down the length of the tube, and the speed at which it travels is the speed of sound. $\endgroup$ – Solomon Slow Mar 27 '19 at 18:25
  • $\begingroup$ Can someone help me with the other questions as well? $\endgroup$ – Lucifer Mar 27 '19 at 19:12

Air is soft and springy- if you squeeze it and let go, it bounces back. In addition, air has mass- if you set a volume of it moving, it wants to keep on moving.

With these two ideas in mind, it is easy to see how waves move through the air. At the piston end of your tube, when the piston moves to the right, it squeezes the air right in front of it and sets some of it into motion. When the piston stops, the air you squeezed springs back and the air you set into motion wants to keep going. In springing back, that volume of air squeezes its nearest neighbor and compresses it- and sets some of it in motion too. Meanwhile, the air you originally set into motion presses against its nearest neighbor, setting some of it in motion and squeezing it a bit as well.

What you get, then, is a wave traveling down the tube, in which parts of the wave are squeezing and unsqueezing and parts of it are moving to and fro. The math is far more complicated than this, but this is the basic idea.

By the way, the squeeziness of the air and its mass per unit volume establish the speed at which the wave propagates. For air, that speed is about 1100 feet per second.

  • $\begingroup$ I still don't get it. Okay so first the piston moves to right and compresses layers of air next it essentially displacing the air molecules from their equilibrium position. This compressed layer then pushes against the adjacent layers setting them to motion, when I then pull the piston left I create a sort of low pressure vacuum which draws in the layers of air it had pushed earlier and this way a wave is set up. If this is true then how displacement and pressure are out of phase by π/2. $\endgroup$ – Lucifer Mar 27 '19 at 19:33
  • $\begingroup$ this is exactly right. are you sure that displacement and pressure are out of phase? $\endgroup$ – niels nielsen Mar 28 '19 at 1:31
  • $\begingroup$ Yes every book seems to have the two out of phase( fox, Crawford etc) $\endgroup$ – Lucifer Mar 28 '19 at 4:20
  • $\begingroup$ Hmm, i'll contemplate this and add anything I think up overnight! $\endgroup$ – niels nielsen Mar 28 '19 at 5:20

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