4.6 Radiation of Sound from Brass Instruments
185
necessarily radiate from the same point, however: the change in boundary conditions
at the bell exit results in energy transfer from the spherical mode to higher (nonspherical) modes, altering the shape of the wavefronts (Benade and Jansson 1974;
Jansson and Benade 1974).
In circumstances in which the radiated sound field can be well approximated by
an isotropic spherical wave, the common centre of the spherical wavefronts can be
described as the ‘acoustic centre’ of the instrument (López-Carromero 2018). The
nature of the pressure fields radiated by real brass instrument bells, and the validity
of the concept of an acoustic centre for brass instruments, will be explored further in
Sects. 4.6.4–4.6.6. In Sect. 4.6.4 the near fields in front of brass instrument bells in
the low-amplitude linear acoustic regime are discussed. High-speed photographs of
shock waves in the near fields at amplitudes typical of ‘brassy’ playing are analysed
in Sect. 4.6.5. In Sect. 4.6.6 the directional characteristics of brass instruments in the
far field are reviewed.
4.6.4 Mapping the Radiation Fields of Brass Instruments
The way in which the nature of the radiated sound field near the bell of a trombone
changes with frequency is illustrated by the pressure maps in Fig. 4.78 (Kemp et al.
2017). The maps in the left-hand column of this figure are derived from calculations
using a multimodal theory. The input to the instrument was taken to be a sinusoidal
signal with the specified frequency. The calculations were performed both inside
and outside the bell, the last 10 cm of which is shown by the magenta curve in each
map.
The right-hand column of Fig. 4.78 displays corresponding maps measured
experimentally using a vertical linear array of 23 microphones in an anechoic
chamber. The array was stepped along the horizontal instrument axis to record the
acoustic pressure at different distances from the bell. A horn loudspeaker driver
at the input to the instrument generated a swept sine pressure signal, which was
repeated at each step of the microphone array. From these measurements it was
possible to derive values of the magnitude and phase of the pressure at each
measured point for any frequency in the range of the sine sweep (López-Carromero
2018).
The real amplitude of the acoustic pressure is represented by the colour scale in
these maps, which are thus snapshots of the pressure distribution in the radiation
field at a particular instant. A wave crest is represented by a colour towards the
yellow (positive) end of the scale, while a trough is represented by a colour towards
the blue (negative) end of the scale. The contours in the experimental maps are
interpolated from discrete measurements on a relatively coarse grid, but broadly
confirm the multimodal predictions.
Figure 4.78a and b illustrate the pressure distribution for the relatively low input
frequency of 500 Hz. The free space wavelength at this frequency is 0.69 m, so the
length of the scanned region is just under half a wavelength. The growing bulge as
185
necessarily radiate from the same point, however: the change in boundary conditions
at the bell exit results in energy transfer from the spherical mode to higher (nonspherical) modes, altering the shape of the wavefronts (Benade and Jansson 1974;
Jansson and Benade 1974).
In circumstances in which the radiated sound field can be well approximated by
an isotropic spherical wave, the common centre of the spherical wavefronts can be
described as the ‘acoustic centre’ of the instrument (López-Carromero 2018). The
nature of the pressure fields radiated by real brass instrument bells, and the validity
of the concept of an acoustic centre for brass instruments, will be explored further in
Sects. 4.6.4–4.6.6. In Sect. 4.6.4 the near fields in front of brass instrument bells in
the low-amplitude linear acoustic regime are discussed. High-speed photographs of
shock waves in the near fields at amplitudes typical of ‘brassy’ playing are analysed
in Sect. 4.6.5. In Sect. 4.6.6 the directional characteristics of brass instruments in the
far field are reviewed.
4.6.4 Mapping the Radiation Fields of Brass Instruments
The way in which the nature of the radiated sound field near the bell of a trombone
changes with frequency is illustrated by the pressure maps in Fig. 4.78 (Kemp et al.
2017). The maps in the left-hand column of this figure are derived from calculations
using a multimodal theory. The input to the instrument was taken to be a sinusoidal
signal with the specified frequency. The calculations were performed both inside
and outside the bell, the last 10 cm of which is shown by the magenta curve in each
map.
The right-hand column of Fig. 4.78 displays corresponding maps measured
experimentally using a vertical linear array of 23 microphones in an anechoic
chamber. The array was stepped along the horizontal instrument axis to record the
acoustic pressure at different distances from the bell. A horn loudspeaker driver
at the input to the instrument generated a swept sine pressure signal, which was
repeated at each step of the microphone array. From these measurements it was
possible to derive values of the magnitude and phase of the pressure at each
measured point for any frequency in the range of the sine sweep (López-Carromero
2018).
The real amplitude of the acoustic pressure is represented by the colour scale in
these maps, which are thus snapshots of the pressure distribution in the radiation
field at a particular instant. A wave crest is represented by a colour towards the
yellow (positive) end of the scale, while a trough is represented by a colour towards
the blue (negative) end of the scale. The contours in the experimental maps are
interpolated from discrete measurements on a relatively coarse grid, but broadly
confirm the multimodal predictions.
Figure 4.78a and b illustrate the pressure distribution for the relatively low input
frequency of 500 Hz. The free space wavelength at this frequency is 0.69 m, so the
length of the scanned region is just under half a wavelength. The growing bulge as