Chapter 4
After the Lips: Acoustic Resonances and
Radiation
In almost all instruments of the brass family, the fluctuating air stream from the
buzzing lips enters a tube whose length is much greater than its largest diameter.
The form and scale of the tube determine the resonant properties of the air column
contained within the instrument and the nature of the sound radiated from it.
In Sect. 4.1 the relationship between standing waves and acoustic resonances is
explained. The distinction is made between time domain and frequency domain
descriptions of the acoustic processes in brass instruments, and the related concepts
of impulse response and input impedance are introduced. Experimental techniques
for measuring the input impedance of a brass instrument are described in Sect. 4.2,
and approximate methods for calculating this important quantity are discussed in
Sect. 4.7. Section 4.3 includes a review of the different types of bore profile which
are found in brass instruments, and a discussion of the influence of the mouthpiece,
mouthpipe, cylindrical and conical sections of tubing and flaring bell on intonation
and timbre. Section 4.4 provides a brief introduction to tonehole labrosones, and
mutes for brass instruments are described in Sect. 4.5. The nature of sound radiation
from brass instruments is reviewed in Sect. 4.6.
4.1 Internal Sounds in Brass Instruments
The sounding pitches available on a brass instrument are strongly influenced by
the way in which sound waves travel through the air inside the instrument. Any
hollow object with at least one hole in its wall has the property that a sound wave
with the right frequency can elicit a strong response in the enclosed air. This is
the characteristic behaviour of an acoustic resonator: the frequency of maximum
response is called the resonance frequency, and the pattern of pressure variation
at resonance is described as an acoustic mode. Almost all members of the brass
© Springer Nature Switzerland AG 2021
M. Campbell et al., The Science of Brass Instruments, Modern Acoustics and Signal
Processing, https://doi.org/10.1007/978-3-030-55686-0_4
101
After the Lips: Acoustic Resonances and
Radiation
In almost all instruments of the brass family, the fluctuating air stream from the
buzzing lips enters a tube whose length is much greater than its largest diameter.
The form and scale of the tube determine the resonant properties of the air column
contained within the instrument and the nature of the sound radiated from it.
In Sect. 4.1 the relationship between standing waves and acoustic resonances is
explained. The distinction is made between time domain and frequency domain
descriptions of the acoustic processes in brass instruments, and the related concepts
of impulse response and input impedance are introduced. Experimental techniques
for measuring the input impedance of a brass instrument are described in Sect. 4.2,
and approximate methods for calculating this important quantity are discussed in
Sect. 4.7. Section 4.3 includes a review of the different types of bore profile which
are found in brass instruments, and a discussion of the influence of the mouthpiece,
mouthpipe, cylindrical and conical sections of tubing and flaring bell on intonation
and timbre. Section 4.4 provides a brief introduction to tonehole labrosones, and
mutes for brass instruments are described in Sect. 4.5. The nature of sound radiation
from brass instruments is reviewed in Sect. 4.6.
4.1 Internal Sounds in Brass Instruments
The sounding pitches available on a brass instrument are strongly influenced by
the way in which sound waves travel through the air inside the instrument. Any
hollow object with at least one hole in its wall has the property that a sound wave
with the right frequency can elicit a strong response in the enclosed air. This is
the characteristic behaviour of an acoustic resonator: the frequency of maximum
response is called the resonance frequency, and the pattern of pressure variation
at resonance is described as an acoustic mode. Almost all members of the brass
© Springer Nature Switzerland AG 2021
M. Campbell et al., The Science of Brass Instruments, Modern Acoustics and Signal
Processing, https://doi.org/10.1007/978-3-030-55686-0_4
101