Superposition of imploding double-layer plane waves explains why cone reflection flips pulse phase
Evidence
We start with a plane pulse consisting of a double layer—a compression followed directly behind by a rarefaction (figure 16.6, left). We construct a spherical imploding wave out of these by adding them up coming from every direction all at once, keeping all the double layers the same distance from a central point. When all the plane waves are added, the inner (orange) compression survives, but the outer (blue) rarefaction gets canceled out by overlapping with orange compression regions. Where orange and blue overlap in equal amounts, the result is white (neutral pressure). Each plane wave translates along at the speed of sound in the direction perpendicular to itself, but suddenly, after they all simultaneously pass through ground zero, the blue rarefaction regions find themselves on the inside of the now expanding sphere, whereas before they were on the outside. The blue regions now survive the superposition of all the waves, and orange has turned to blue! — Eric J. Heller, Why You Hear What You Hear- An…, 1464
Categorization
Category: Definitional Content
- DEFINE: Gives a constructive, rigorous-seeming mechanism for the counterintuitive phase flip at a conical apex, showing why the cone behaves like an open end.
Related
- A cone’s apex turns what would be a wave node into an antinode (similarity 0.79)
- Waves split into reflected and refracted parts at impedance-mismatched interfaces (similarity 0.78)
Broader Connections
- Waves transitioning from bounded to unbounded space create interfering reflections
#corroborates(0.75) — David Howard, Jamie Angus, coustics and Psychoacoustics, 2199 - Waves split into reflected and refracted parts at impedance-mismatched interfaces
#expands(0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 207 - Reflection phase at solid versus open boundaries differs fundamentally.
#corroborates(0.72) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 355 - Impedance discontinuities split an arriving wave into reflected and transmitted parts
#corroborates(0.72) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 235