A stopped pipe sounds an octave lower than an open pipe of equal length

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

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 considering 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 T0(stopped) = fundamental period of stopped pipe Ls = length of the stopped pipe and c = velocity of sound Therefore: If an open pipe and a stopped pipe are the same length, what is the relationship between their f0 values? — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1168

Categorization

• DEFINE: Explains the octave relationship between stopped and open pipes, a foundational psychoacoustic fact about pitch perception tied to pipe length.
• SHARE: Worth sending to a musician or instrument-maker friend who would appreciate why covering the end of a pipe drops pitch an octave.
• corroborated: 5 independent passages support this claim — David Howard, Jamie Angus, coustics and Psychoacoustics, 1198; David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1168
• XREF: connects to: A closed pipe end reflects a pulse with no energy loss without moving; Short wavelengths escape open pipe ends while long wavelengths reflect back; One closed and one open pipe end supports only odd quarter-wavelength standing waves (+7 more)

Broader Connections

• A closed pipe’s first mode sits an octave below an open pipe’s #corroborates (0.95)