Suppose you have a long tube filled with air, and a piston is moving to and fro in a periodic manner. Why would air pressure variations be created near the end of the piston where it's oscillating ? (I am studying this in sound chapter beginning and I couldn't understand this)
The book is claiming something like this would happen:
I don't have the intuition behind why this happens. If the tube is sufficiently long, then my intuition tells that there would be no pressure variation at all, and moreover pushing/pulling the piston wouldn't require any force. Is my intuition incorrect ?
Best Answer
Remember what causes pressure.
In an ideal gas, pressure is given by:
$P = \dfrac{N R T}{V}$
Where $N$ is the number of particles (atoms or molecules for example), $T$ the temperature, $V$ the volume and $R$ the ideal gas constant.
Now look at your sketch that I modified a bit:
Notice how the gas that was initially contained in a volume $V_1$ is now contained in a volume $V_2 < V_1$ as a result of the motion of the piston.
As the piston moves and pushes particles forward, the number of particles $N$ stays the same, but the volume decreases, hence the pressure increases locally.
Inversely, as the piston moves backward particles rapidly expand into the newly available space. Thus the local density $n = \dfrac{N}{V}$ decreases, hence the local pressure decreases.
Now let's clarify some points that you have been asking:
1) If the tube is sufficiently long, then my intuition tells that there would be no pressure variation at all?
The lenght of the tube has nothing to do with the fact that locally, a perturbation pressure is created as a result of the motion of the piston.
You are right when you imply that a little variation of volume $\Delta V$ over a great volume $V_{tot} \gg \Delta V$ would only create a tiny variation of pressure $\Delta P$ over the whole tube, once it has reached its new equilibrium. However, we are interested here in what happens locally, in the small volume right next to the piston. We are interested in the dynamics of the fluid, which you have to distinguish with what would be a quasistatic evolution of the gas inside the tube.
Your intuition would be true if the pressure perturbation was traveling at an infinite speed, which is not the case (due to friction, inertia, etc...). In fact it does travel with a velocity equal to sound speed.
2) Why the gas particles are not moving away from their original position but rather oscillating in their original position?
Gas particles are trying to move away, but as they are displaced they encounter their direct neighbours, which prevents them from expanding further. As a consequence they can only communicate that perturbation pressure to the next slab of gas, and so on.
3) Why would the" pressure change wave" propagate through the tube instead of staying in the original position?
As you can infer from 2), the pressure perturbation pressure propagates along the tube as adjacent slabs of gas are communicating that overpressure to each other. That is all acoustic waves are about.