Standing waves in pipes occur only at odd multiples of the lowest frequency

Evidence

A standing wave cannot exist with even numbers of quarter wavelengths, as this would require a pressure node or antinode at both ends as shown in Figures 1.32 and 1.35. The frequencies that can support standing waves exist at odd multiples of the lowest standing wave frequency. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 410

Categorization

• DEFINE: The odd-multiple constraint is the core rule for which frequencies resonate in bounded acoustic systems — essential factual grounding.
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 410
• XREF: connects to: A stopped cylindrical pipe supports only odd-numbered modes — David Howard, Jamie Angus, coustics and Psychoacoustics, 1241; String and pipe resonance differ in transverse versus longitudinal wave motion — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1132