Pipe bore constriction shifts mode frequencies depending on standing-wave node position

Evidence

A constriction at a pressure node (velocity antinode) has the effect of reducing 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 that produces a greater opposition 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). By the same token, the effect of locally enlarging a pipe will be exactly opposite to that of constricting it. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1222

Categorization

• DEFINE: Clarifies the mechanism by which pipe constriction/enlargement alters specific mode frequencies via pressure node/antinode positions.
• XREF: connects to: Pipe constrictions shift mode frequencies up or down depending on node position — David Howard, Jamie Angus, coustics and Psychoacoustics, 1251; Standing wave node positions let one predict bore-change effects on mode frequencies — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1223; A local bore constriction can tune individual pipe modes separately — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1225 (+4 more)

Broader Connections

• Pipe constrictions shift mode frequencies up or down depending on node position #corroborates (0.97) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1251
• Local bore changes tune instrument modes by their position relative to pressure nodes #expands (0.92)
• Standing wave node positions let one predict bore-change effects on mode frequencies #expands (0.88) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1223
• A constriction at a pressure node slows air and lowers resonant frequency #expands (0.86) — Eric J. Heller, Why You Hear What You Hear- An…, 1641
• Constricting a tube at a pressure node lowers the modal frequency #qualifies (0.85)
• A local bore constriction can tune individual pipe modes separately #expands (0.84) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1225