Brass instruments are lip-driven pressure valves that behave acoustically like stopped pipes.

Evidence

In a complete brass instrument, it is possible through the use of an appropriately shaped bell, mouthpiece and mouthpipe to construct an instrument whose modes are frequency shifted from the odd-only modes of a stopped cylindrical pipe to being very close to a complete harmonic series. In practice, the result is a harmonic series in which all modes are within a few percent of being integer multiples of a common lower-frequency value except for the first mode itself, which is well below that lower-frequency value common to the higher modes, and therefore it is not harmonically related to them. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250 (#expands, via linked claim)

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 (#exemplifies, via linked claim)

Categorization

• XREF: connects to: Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250; Trumpet valves combine with lip synchronization to expand pitch range; Reed pipes behave as stopped-end resonators, unlike open-ended flue pipes — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1205 (+4 more)

Broader Connections

• Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series #expands (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250
• A stopped pipe sounds an octave lower than an open pipe of equal length #exemplifies (0.80) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1198
• Trumpet valves combine with lip synchronization to expand pitch range #expands (0.78)
• Reed pipes behave as stopped-end resonators, unlike open-ended flue pipes #qualifies (0.72) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1205