Wave Frequency in Piston: Pressure Variation & Adiabatic Compression

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The fundamental frequency of oscillation in a piston is determined by the equation ν = 1/4L √(γp/ρ), where p represents the pressure, γ accounts for adiabatic compression, and ρ is the gas density. The discussion raises a question about the assumption of constant pressure during gas compression. It clarifies that the pressure used in the formula should be the equilibrium pressure of the gas, not the varying pressure during compression. This distinction is crucial for accurately applying the formula in practical scenarios. Understanding this concept is essential for analyzing wave behavior in piston systems.
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When you have a wave in sound inside a piston of length L, A.P. French says that the fundamenal frequency \nu of an oscillation is given by

\nu = 1/4L \sqrt{(\gamma p / \rho)}

Where p is the pressure, \gamma is the factor that accounts for adiabatic compression of the gas, and \rho is it's density.

My question is this : doesn't the pressure p vary as you compress the gas? How can you assume it to be constant?
 
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Hold up. I think I got it. That's not ANY pressure that you plug into that formula, it's the pressure when the gas is at equilibrium.
 
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