Rarefaction and condensation… or should it be compression?

One annoyance in acoustics we’ve had for over three decades is the use of the term “condensation” (the opposite of rarefaction) when describing acoustic wave propagation in gaseous fluids. Instead, I’ve always preferred the term “compression” instead of “condensation,” as it more accurately describes the thermal process taking place, whether the propagation is taking place in an isothermal (P*V)=constant or more commonly adiabatic (P*V)γ=constant thermodynamic process; where γ = 1.4 for an adiabatic process, and unity for an isothermal (such as an ideal gas law) process, with the exponential notation typically omitted.

My reason for this change is that the term “condensation” implies a phase change from gas to liquid, such as occurs  in a condenser in a refrigeration circuit or boiler steam circuit. Since (in most cases) we are dealing with adiabatic propagation, the temperature actually increases when gases are compressed, moving away from the phase change curve.

For the less common case of isothermal propagation, such as through fiberglass insulation, then condensation could (theoretically) occur; however, I would still prefer to call it “compression” as even at the linearity limit of an acoustic wave of 194 dB intensity (which is 14.7 psia or 1000 millibars), gas → liquid phase change will not occur… But it will be guaranteed to rupture your eardrums. [Hat tip to Wayne Staab PhD for pointing this out.]

Update: It turns out I’m not the only one using this terminology: While looking through the Audio Related Things page of the late Georgia Tech Electrical Engineering Professor W Marshall Leach, I ran across  An Electroacoustic Analysis Of Transmission Line Loudspeakers, the 2007 Georgia Tech PhD thesis by Robert Allen Robinson Jr of which Dr Leach was one of the advisors. Dr Robinson too uses the “rarefaction and compression” nomenclature throughout, including on page 100 (PDF page 117). Here’s an animation of the process:

compression-rarefaction animation

Compression — Rarefaction Animation

 

Adiabatic and Isothermal descriptions

 

As a side note, loudspeaker engineers trained by Georgia Tech professors Eugene Patronis &/or W Marshall Leach (both Fellows of the Audio Engineering Society) will quickly recognize that the way to increase the box volume of a loudspeaker is to pack it with fiberglass for a volume increase of about 1.2x (using a  γ ≈ 1.2), as the acoustic waves will propagate in a manner in between adiabatic and isothermal… At the expense of lowering box Q, which is Not Good for the unassisted 4th order vented response. Of course, you can pack your cabinet with steel wool for a  γ approaching 1.4, but then it gets messy with the driver magnet. For a more thorough discussion on this, including frequency dependence and derivation, please see pages 100-101 (PDF pages 117-118) in  An Electroacoustic Analysis Of Transmission Line Loudspeakers, the 2007 Georgia Tech PhD thesis by Robert Allen Robinson Jr~

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About the author

Dan Schwartz

Electrical Engineer, via Georgia Tech

2 Comments

  1. David
    September 24, 2012 at 4:12 pm

    How would you explain the use of rarefaction, compression and condensation in a standing wave. I believe this is where the terms rarefaction and compression actually represent the same process, the opposite of which is condensation.


    • Dan Schwartz
      September 24, 2012 at 11:58 pm

      No, David: Rarefaction is defined as a local area where the pressure is lower (“rarefied”) than average; while compression and condensation — Which are (improperly) interchanged, is where the pressure is higher than average.

      Condensation implies a gas –> liquid phase change, which does not occur with acoustic waves — Think of your refrigerator with the black condenser coils on the back, where the refrigerant that was evaporated at the expansion valve condenses and releases the heat absorbed in the evaporator coils; and is then pumped by the compressor for another trip around the circuit.


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