An open pipe’s fundamental period equals twice its length divided by wave speed

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 (#complicates, via linked claim)

Categorization

• XREF: connects to: Open pipe ends invert pulse polarity while closed ends preserve it; A stopped pipe sounds an octave lower than an open pipe of equal length — David Howard, Jamie Angus, coustics and Psychoacoustics, 1198; Open-open tubes support standing waves with the same half-wavelength rule (+3 more)

Related

• Open pipe ends invert pulse polarity while closed ends preserve it (similarity 0.94)
• A stopped pipe sounds an octave lower than an open pipe of equal length (similarity 0.92)
• Open and stopped organ pipes correspond to open-open and open-closed acoustic tubes. (similarity 0.88)
• An open-open pipe’s modes form a complete harmonic series at integer multiples (similarity 0.84)
• Stopped organ pipes sound the same pitch at half the length (similarity 0.82)
• Pipe length sets pitch while diameter and material shape harmonic strength (similarity 0.82)
• An open pipe end inverts a sound pulse’s sign via a reflected rarefaction (similarity 0.82)
• Open and stopped organ pipes audibly start on different overblown harmonics (similarity 0.81)
• The human vocal tract behaves acoustically as a stopped pipe about 17.5 cm long. (similarity 0.81)
• Doubling all pipe dimensions lowers its fundamental tone by an octave (similarity 0.81)
• A stopped cylindrical pipe supports only odd-numbered modes (similarity 0.80)
• Cylindrical stopped-pipe bores support only odd-numbered modes, forcing extra finger holes (similarity 0.80)
• Open-open tubes support standing waves with the same half-wavelength rule (similarity 0.80)
• The player’s lips form a variable double reed making brass a stopped-pipe acoustics (similarity 0.80)
• Open tube ends preferentially transmit high frequencies and reflect low ones, smearing echoes. (similarity 0.79)

Broader Connections

• A stopped pipe sounds an octave lower than an open pipe of equal length #complicates (0.82) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1198
• Open-open tubes support standing waves with the same half-wavelength rule #corroborates (0.80)
• Open-open and open-closed tubes produce different harmonic series #expands (0.78)
• Pipe length sets pitch while diameter and material shape harmonic strength #exemplifies (0.78)
• Open pipe ends reflect low frequencies but pass high frequencies #expands (0.75)