At an open boundary, pressure equals zero while velocity doubles.

Evidence

This is equivalent to the reflection of a wave in the reverse direction in which the phase of the wave is reversed, because it has started as a stretching of the “springs,” or rarefaction, as opposed to a compression. Figure 1.24 shows this effect using the golf ball-and-spring model in which the unbounded region is modeled as having no springs at all. An interesting effect also occurs in this case due to the fact that the wave has to change direction. That is, the mass that is connected to the unbounded region is moving with twice the velocity compared to masses well away from the boundary. This occurs because the pressure components associated with the reflected (bounced back) wave are moving in contrary motion to the pressure components of the incoming wave due to the change of phase in the reflected pressure components. In acoustic terms, this means that while the pressure component at the reflecting boundary is zero, the velocity component is twice as large. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 354

Categorization

Category: Causal Relationships

• DEFINE: Explains why the pressure node and velocity antinode coincide at an open-ended boundary, a core boundary-condition concept for standing waves in pipes.

Related

• Sound reflecting off a hard boundary has zero particle velocity (similarity 0.85)
• Multiple open holes jointly shift the effective pressure node (similarity 0.83)
• Hard boundaries reflect sound because pressure energy cannot cross a zero-velocity point. (similarity 0.82)
• Sound wave molecules have zero velocity at compression peaks due to inertia (similarity 0.81)
• Reflection phase at a boundary depends on whether acoustic impedance rises or falls (similarity 0.78)

Broader Connections

• Medium density and elasticity shape the pressure-velocity amplitude relation #expands (0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 165