Standing waves in tubes need specific node-antinode patterns at boundaries

Evidence

The second is more interesting and consists of one hard boundary and one bound–unbound boundary, and is shown in Figures 1.37 and 1.38. In this situation there is a pressure node at the bound–unbound boundary and a pressure antinode at the hard boundary. The effect of this is to allow a standing wave to exist when there is only an odd number of quarter wave­ lengths between the two boundaries. — David Howard, Jamie Angus, coustics and Psychoacoustics, 404

Categorization

• DEFINE: Clarifies how quarter-wavelength standing waves arise when one boundary is hard and the other bound-unbound.