Wall losses, not radiation, dominate resonance damping in narrow pipes

Evidence

According to figure 16.1, the losses due to sound radiation alone would have given a much higher Q, because the reflection amplitude for a 0.95-cm-radius tube at 1180 Hz is 98%. (This is hard to read off figure 16.1 but we recalculated the number using Levine and Schwinger’s theory.) This corresponds to a 4% energy loss for every encounter with the open end, occurring once per round-trip of the pipe. According to the formula in section 10.3, Q = 2π energy remaining/energy lost (per cycle), and we should have had Q = 2π(1/0.04) ~ 157. The measured Q is more than five times smaller, so we can be certain the Q is limited by wall losses and not sound radiation. This tube is far to the left, in the waxing region on the resonance advantage curve (see equation 10.13 and figure 10.10). — Eric J. Heller, Why You Hear What You Hear- An…, 1448

Categorization

Category: Contrarian or Surprising Claims

• XREF: Pays off the Q formalism built up in section 10.3 and the resonance advantage curve — a strong callback demonstration.

Related

• Radiation losses are negligible compared to wall losses in narrow pipes (similarity 0.91)
• Pipe walls raise air impedance by reflecting pressure pulses back in phase (similarity 0.84)
• Narrower pipes raise acoustic impedance through in-phase wall reflections (similarity 0.82)
• An open pipe end only reflects sound when an impedance mismatch exists there (similarity 0.81)
• Adding damping to a resonance paradoxically makes it more audible by widening its bandwidth (similarity 0.80)
• A sound pulse passes an open pipe end unreflected when matching pressure exists outside (similarity 0.80)
• Any pipe diameter change causes partial sound reflection at the junction (similarity 0.79)
• Wall friction and resonance oppose each other in determining instrument sound radiation. (similarity 0.79)
• Well-damped low-Q resonances are easier to hear than high-Q ones. (similarity 0.79)
• Resonant power dissipation actually grows when damping decreases (similarity 0.79)
• Open tube ends preferentially transmit high frequencies and reflect low ones, smearing echoes. (similarity 0.79)
• Bounded sound waves change impedance with tube area, causing reflections (similarity 0.78)

Broader Connections

• Wall damping grows with frequency only as the square root #expands (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 1444
• Adding damping to a resonance paradoxically makes it more audible by widening its bandwidth #complicates (0.80) — Toole, Floyd E, Sound reproduction- the acoustics and…, 498
• Pipe walls raise air impedance by reflecting pressure pulses back in phase #complicates (0.78) — Eric J. Heller, Why You Hear What You Hear- An…, 121
• Horn bells boost lower frequencies where wall friction dominates resonance enhancement #complicates (0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 1708
• A closed pipe end reflects a pulse with no energy loss without moving #complicates (0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 111