Woodwind instruments

Wind instruments/aerophones

Pressure changes are generated directly in air, rather than by radiation from a vibrating structure. Wall material is therefore relatively unimportant.

Air jet sound generator

Acoustical open end (flute)

Reed sound generator

Acoustical closed end (oboe)

Closed end reflection

A pressure wave travelling forwards or backwards in a woodwind tube is reflected with no change of phase when it arrives at a close end.

Open end reflection

A pressure wave travelling forwards or backwards in a woodwind tube is reflected with a phase change of 180 degrees when it arrives at an open end

Standing wave

The sum of a wave travelling forwards and a wave travelling backwards.

Pressure node in a standing wave air column

A fixed point of zero pressure variation

Pressure antinode in a standing wave air column

A fixed point of maximum pressure variation

Distance of nodes in a cylindrical tube

The distance between two adjacent pressure nodes is a half wavelength and the distance between a pressure node and an adjacent antinode is a quarter wavelength

Frequency of nth standing wave in a cylindrical tube

fn = n (c/2L)

Frequencies of acoustic modes in cylindrical tube

In a a cylindrical tube of length L, open at both ends, the frequencies of the acoustics modes are members of a complete harmonic series.

Frequency of nth standing wave in a cylindrical tube closed at one end

fn = (2n - 1) c/4L

Frequencies of acoustic modes in cylindrical tube closed at one end

In a cylindrical tube of length L, closed at one end and open at the other, the frequencies of the acoustic modes are odd members only of a harmonic series.

Frequencies of nth standing wave in conical tube

fn = n (c/2L)

Frequencies of acoustic modes in a conical tube closed at the apex

In a conical tube of length L, closed at the apex and open at the other end, the frequencies of the acoustic modes are members of a complete harmonic series.

Acoustic input impedance at antinodes

Peaks in the input of impedance Z corresponds to pressure antinodes at the input

Acoustic input impedance at nodes

Dips in the input impedance Z corresponds to pressure nodes at the input

End correction

At the open end of a cylindrical tube of diameter D, the pressure node is a distance deltaL = 0.3D beyond the exit plane.

Tonehole

• When a tonehole is opened near the output end of an instrument, low frequency waves are reflected just beyond the open hole.

• The pressure node moves towards the hole, shortening the wavelength and raising the pitch.

• If the hole diameter is increased, the node moves closer to the hole.

Cutoff frequency

• Above a cutoff frequency which depends on the dimensions of the open hole, the wave continues to propagate beyond the hole.

• The effect of opening a tonehole on the playing pitch is therefore smaller and less predictable for notes above the cutoff frequency.

Flow controlled

The air jet sound generation mechanism is …

Jet injected into stationary fluid

A jet injected into a stationary fluid is inherently unstable. Small perturbations are convected as a hydrodynamic wave along the jet, growing in amplitude.

Hydrodynamic wave

The hydrodynamic wave in a free jet becomes chaotic. A stable oscillation can be created when the jet is coupled to a transverse acoustic pressure field.

Airjet flow for flute

Air jet flow into the flute is greatest when the acoustic pressure is high, ensuring net energy transfer to standing waves.

Overblowing

On the flute, overblowing from the first register to the second without changing the fingering raises the pitch by an octave.

Pressure controlled

The reed sound generation mechanism is called …

Air flow destabilising

Air flow destabilises the reed, which locks into vibration coupled primarily to one end of the acoustic modes of the air column.

Pressure differences across the reed

As the pressure difference across the reed increases slowly, an inward striking reed closes while an outward striking reed opens.

Inward striking reed

Woodwind reed, increasing mouth pressure closes the reed

Overblowing on the clarinet

On the clarinet, overblowing from the first register to the second without changing the fingering raises the pitch by a twelfth

Overblowing on the oboe

On the oboe, overblowing from the first to the second register without changing the fingering raises the pitch by an octave.