When is it appropriate to use zero normal stress boundary conditions when solving the acoustic wave equation. That is when the pressure is equal to zero.


1 Answer 1


Strictly speaking: never. Outside the idealized models there are always at least a bit of radiation impedance so the pressure on the boundary is not truly zero.

But let's focus on idealized models. Usually the zero pressure boundary condition is used for open ends of the waveguides or for the free surfaces of solid bodies.

Typical illustrative example would be the loose end of the string: there is nothing (e.g. no bridge) which can provide a support for string stretching. Therefore the tension (analogy of pressure) must be zero and all the energy goes into displacement.

  • $\begingroup$ How accurate is the p=0 approximation for open ended waveguides? $\endgroup$
    – mdornfe1
    Oct 30, 2015 at 17:19
  • $\begingroup$ If you seek for a standing wave, than is is sufficient. But if you want examine the radiation, then you need to be more careful. Study the wave reflection at the borderline of enviroments. It would be almost the limit case. $\endgroup$ Oct 30, 2015 at 21:11
  • $\begingroup$ So I have a somewhat tangential question. Do standing waves even exist in real life? It seems like they're just an idealization that approximate a situation with low dissipation. $\endgroup$
    – mdornfe1
    Nov 2, 2015 at 17:12
  • $\begingroup$ Let's say it is a highly useful model, very well valid in significant amount of cases. Of course, there are no pure infinite impedance to make the total reflection and so on. $\endgroup$ Nov 2, 2015 at 20:49

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