Pipe constrictions shift mode frequencies up or down depending on node position

Evidence

A constriction at a pressure node (velocity antinode) has the effect of reduc­ ing the flow at the constriction since the local pressure difference across the constriction has not changed. Benade (1976) notes that this is equivalent to raising the local air density, and the discussion in Chapter 1 indicates that this will result in a lowering of the velocity of sound (see Equation 1.1) and therefore a lowering in the mode frequency (see Equations 4.7 and 4.9). A constriction at a pressure antinode (velocity node), on the other hand, provides a local rise in acoustic pressure which produces a greater oppo­ sition to local airflow of the sound waves that combine to produce the standing wave modes. This is equivalent to raising the local springiness in the medium (air), which is shown in Chapter 1 to be equivalent for air in Young’s modulus (Egas), which raises the velocity of sound (see Equation 1.5) and therefore raises the mode frequency (see Equations 4.7 and 4.9). — David Howard, Jamie Angus, coustics and Psychoacoustics, 1251

Categorization

• DEFINE: The pressure-node vs pressure-antinode distinction in standing waves is a core psycho-acoustics concept: density vs springiness as alternative mechanical models of the same wave disturbance.
• XREF: connects to: Pipe bore constriction shifts mode frequencies depending on standing-wave node position — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1222