Brass Acoustics · Manuscript excerpt
The Lip-Reed Valve
How lip motion, airflow and the instrument work together
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A cornet, trumpet or flugelhorn is a pipe with a mouthpiece at one end and a bell at the other. It contains a column of air. The player supplies air under pressure through the opening between the lips. That opening repeatedly widens and narrows, producing pulses of airflow into the mouthpiece. The pulses build up the vibration of the air column. Its changing air pressure in the mouthpiece then changes the forces on the lips and helps sustain their repeated opening and closing.
The lips are called a lip-reed valve because their movement regulates the passage of air. The opening between their opposing surfaces is the aperture. When those surfaces separate, air passes through; when they meet completely, through-flow stops. The muscles establish and adjust the lip configuration. They do not contract separately for every vibration.
How the vibration begins and continues
Before the onset, with the instrument at rest, air pressure in the mouthpiece and pipe is atmospheric. The player raises the air pressure in the mouth. The resulting pressure difference loads the exposed lip tissue.
When this loading displaces and deforms the lips sufficiently to separate their opposing surfaces, a passage opens and air enters the mouthpiece.
The entering air changes the pressure in the cup and starts a pressure wave along the pipe. Air already within the pipe transmits that wave: each region moves and compresses the neighbouring air. The wave travels at the speed of sound. This propagation speed is different from the speed of air flowing through the lip aperture.
The bell flare and opening allow acoustic energy to radiate outwards and produce a returning pressure wave.
The returning wave changes air pressure in the mouthpiece. Thus, after the first airflow pulse, the cup-facing lip surfaces are exposed to an air pressure that changes with the developing vibration of the air column.
The lip movement also deforms the tissue. This deformation produces an elastic restoring force, directed towards the tissue’s equilibrium configuration. During an opening movement that stretches the tissue away from that configuration, the restoring force opposes further opening. The tissue’s mass gives it inertia: a force opposing the opening first slows the movement. The aperture continues widening until the opening velocity reaches zero. If the net force remains directed towards closure, the opposing surfaces then approach one another.
Air pressure within the passage contributes to these forces. In the Bernoulli approximation, pressure does work on the flowing air. Where the air gains speed, its kinetic energy increases and its air pressure decreases.
This approximation neglects density changes and losses. The lower air pressure within the lip passage changes the loading of its opposing surfaces and contributes a closing force. It is the pressure acting over those surfaces that produces the force—not airspeed acting directly on the tissue. The pressure reduction is one contribution to closure; elastic restoring forces and the movement already acquired by the tissue must also be included. Because the passage changes rapidly, ordinary steady-flow Bernoulli does not describe every part of the cycle exactly.
Mouthpiece air pressure changes the loading independently of this passage-pressure reduction. With mouth air pressure maintained, a fall in cup air pressure increases the mouth-to-cup pressure difference; a rise reduces it. These changes alter both the airflow and the force exerted on the exposed lip tissue. Consequently, rising cup air pressure must not be explained merely as “slower air makes the lips close.” Slower air would itself weaken the Bernoulli pressure reduction.
As the opposing surfaces approach, the aperture narrows and the airflow pulse diminishes. At complete contact, through-flow stops. The air column continues vibrating, however, so mouthpiece air pressure continues changing during the closed interval. The tissue also remains deformed and in motion through the contact event. Reopening follows when the combined pressure, elastic and contact forces accelerate the surfaces apart.
The new opening admits another airflow pulse. This pulse enters an air column already vibrating from the preceding pulse and its reflections. When the timing supplies energy to that vibration, its amplitude grows. The growing mouthpiece pressure fluctuations exert stronger alternating forces on the lips, influencing the timing and extent of subsequent openings. This is acoustic feedback: the airflow produces pressure changes in the air column, and those pressure changes alter the lip movement that produces the next airflow pulse.
The build-up starts with the first pressure disturbance; resonance does not switch on after a fixed number of pulses. Growth continues while the supplied acoustic energy exceeds the losses. In a sustained tone, the energy supplied over successive cycles replaces the energy radiated through the bell and dissipated internally.
The player maintains blowing pressure and lip configuration while the rapid pressure–tissue–airflow cycle continues.
Cycles per second and sounding pitch
The repetition frequency of a regular lip cycle corresponds to the sounding fundamental frequency. Written G4 on a B♭ cornet sounds at approximately 349 Hz, giving about 2.86 milliseconds for a complete cycle. Opening, narrowing and any interval of complete contact occur within that time.
The lip tissue has its own mechanical response, determined by its moving mass, stiffness and configuration.
The air column has frequencies at which vibration builds particularly strongly. The sounding frequency results from their coupled behaviour. Changing the lip configuration changes that behaviour; the air column’s pressure feedback helps maintain a stable playing frequency.
Aperture shape, airflow and sound
The aperture has width, height and depth. Its frontal outline may be slit-like, lens-shaped or rounder, but that outline does not reveal the whole passage. Air travels between opposing tissue surfaces whose separation can vary along the passage from the mouth towards the cup. Both that shape and its change during the cycle affect airflow and the pressure acting on the tissue.
Air consumption depends on the volume passing through the aperture over time. Maximum aperture area alone is insufficient: the duration of opening and the changing pressure difference also matter. A measured aperture area therefore cannot be converted into air consumption without further information about the flow.
The repeated airflow pulse contains the fundamental and harmonics, frequency components at whole-number multiples of the fundamental. Changes in pulse shape change their relative strengths. The mouthpiece, air column and bell then affect what reaches the listener. An aperture measurement or calculated spectrum can explain a physical difference; whether that difference is audible requires listening evidence.
Selected manuscript references
Campbell, D. M., Gilbert, J., and Myers, A. (2021). The Science of Brass Instruments. Springer.
Adachi, S., and Sato, M. (1996). Trumpet sound simulation using a two-dimensional lip vibration model. Journal of the Acoustical Society of America, 99(2), 1200–1209. doi:10.1121/1.414601
Giordano, N. (2019). Force on the lips of a trumpet player. Journal of the Acoustical Society of America, 145(3), 1521–1528. doi:10.1121/1.5094763