Open pipe ends invert pulse polarity while closed ends preserve it

Evidence

It is immediately clear that one cycle for the stopped pipe takes twice as long as one cycle for the open pipe if the pipe lengths are equal (ignoring a small end correction which has to be applied in practice). Its fundamental period is therefore double that for the open pipe, and its f0 is therefore half that for the open pipe, or an octave lower. This can be quantified by consid­ ering that the time taken to complete a complete cycle is the time required for the pulse to travel to the other end of the pipe and back twice, or four times the stopped pipe length (see Figure 4.15): where fundamental period of stopped pipe  th of the stopped pipe and velocity of sound c  The natural modes of a pipe are constrained as described in the “stand­ ing waves” section of Chapter 1. — David Howard, Jamie Angus, coustics and Psychoacoustics, 1198 (#corroborates, via linked claim)

Categorization

• XREF: connects to: A closed pipe end reflects a pulse with no energy loss without moving; Pipe walls raise air impedance by reflecting pressure pulses back in phase; Short wavelengths escape open pipe ends while long wavelengths reflect back (+6 more)

Related

• An open pipe’s fundamental period equals twice its length divided by wave speed (similarity 0.94)
• A stopped pipe sounds an octave lower than an open pipe of equal length (similarity 0.91)
• An open pipe end inverts a sound pulse’s sign via a reflected rarefaction (similarity 0.88)
• Open and stopped organ pipes correspond to open-open and open-closed acoustic tubes. (similarity 0.87)
• Open pipe ends invert compression pulses while closed ends preserve them (similarity 0.85)
• Open and closed pipe ends reflect pressure pulses with inverted phase (similarity 0.84)
• Open tube ends preferentially transmit high frequencies and reflect low ones, smearing echoes. (similarity 0.84)
• An open pipe end only reflects sound when an impedance mismatch exists there (similarity 0.84)
• Pipe walls raise air impedance by reflecting pressure pulses back in phase (similarity 0.83)
• A stopped cylindrical pipe supports only odd-numbered modes (similarity 0.83)
• Cylindrical stopped-pipe bores support only odd-numbered modes, forcing extra finger holes (similarity 0.82)
• Woodwind flue instruments act acoustically as pipes open at both ends (similarity 0.81)
• A stopped pipe’s cycle takes twice as many snapshots as an open pipe’s (similarity 0.81)
• Stopped organ pipes sound the same pitch at half the length (similarity 0.81)
• Organ flue pipes divide into open-open and open-closed acoustic types (similarity 0.81)

Broader Connections

• A closed pipe’s first mode sits an octave below an open pipe’s #expands (0.95)
• A stopped pipe sounds an octave lower than an open pipe of equal length #corroborates (0.95) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1198
• Mixed-end tubes resonate only at odd multiples of the fundamental frequency #expands (0.90)
• An open pipe’s fundamental period equals twice its length divided by wave speed #expands (0.90)
• Stopped pipes save space but sacrifice even-numbered harmonics #expands (0.85)