How are sound waves produced? 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:


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*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?

*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?

*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?

*Can someone provide a qualitative description of how a sound wave is produced by sinusoidally moving the piston in the air tube?

 A: 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.
