112
4 After the Lips: Acoustic Resonances and Radiation
maximised when the input is a pressure antinode. If we had chosen a tube length
which was not an odd number of quarter wavelengths, this condition would not have
been satisfied. A pure standing wave with frequency 466 Hz and a pressure antinode
at the input could not exist in such a tube, and it would be difficult for a brass player
to sound the note B 4 on it. In general, for an arbitrary frequency, the acoustic field
can be viewed as a superposition of a standing wave and a travelling wave.
4.1.4 Frequency Domain and Time Domain
In discussing the acoustical behaviour of a brass instrument tube, there are two
different but complementary approaches which can be taken. One is the time domain
approach, which typically focuses on the way in which pressure changes in the
air column develop over time. This method is particularly useful in dealing with
transient phenomena, such as the starting of a new note or transitions between notes.
The other is the frequency domain approach, which examines the behaviour of the
instrument in response to different sine wave frequency components. Frequency
domain techniques are very well adapted to investigating and describing continuously sounded notes.
Although brass players may not talk about time domain and frequency domain
approaches, they are very aware of the corresponding aspects of musical performance. When presented with a new instrument for evaluation, a player will probably
assess its intonation by playing octaves and slow arpeggios over the instrument’s
compass; this is an experimental investigation of its behaviour in the frequency
domain. It is likely that the transient behaviour will be assessed by playing staccato
notes, double-tonguings and trills; this is a typical time domain experiment. The
instrument must not only play in tune, but it must be capable of responding flexibly
to the rapid succession of commands sent to the instrument by the player in a
virtuoso performance (see Sect. 1.2.10).
The picture in Fig. 4.7 showing nodes and antinodes of a standing wave in a
cylindrical tube illustrates one aspect of a frequency domain view of the acoustical
behaviour of the tube. It shows how the tube responds to excitation by a continuous
sinusoidal disturbance at a specific frequency. To complete the frequency domain
picture, it would be necessary to repeat the calculation for many different values of
the frequency.
We have already described a simple but illuminating time domain experiment
which can be carried out on a brass instrument without elaborate scientific equipment. Slapping the palm of the hand on to the open surface of the mouthpiece sends
a pulse down the air column, and a microphone just outside the bell records the
sound radiated by the instrument.
Figure 4.8 was obtained by gently slapping a palm against the mouthpiece rim
on a Conn 8H tenor trombone with the slide in first position. The radiated sound
was recorded using a small lapel microphone whose output was connected to the
external microphone input of a laptop running the free software program Audacity.
4 After the Lips: Acoustic Resonances and Radiation
maximised when the input is a pressure antinode. If we had chosen a tube length
which was not an odd number of quarter wavelengths, this condition would not have
been satisfied. A pure standing wave with frequency 466 Hz and a pressure antinode
at the input could not exist in such a tube, and it would be difficult for a brass player
to sound the note B 4 on it. In general, for an arbitrary frequency, the acoustic field
can be viewed as a superposition of a standing wave and a travelling wave.
4.1.4 Frequency Domain and Time Domain
In discussing the acoustical behaviour of a brass instrument tube, there are two
different but complementary approaches which can be taken. One is the time domain
approach, which typically focuses on the way in which pressure changes in the
air column develop over time. This method is particularly useful in dealing with
transient phenomena, such as the starting of a new note or transitions between notes.
The other is the frequency domain approach, which examines the behaviour of the
instrument in response to different sine wave frequency components. Frequency
domain techniques are very well adapted to investigating and describing continuously sounded notes.
Although brass players may not talk about time domain and frequency domain
approaches, they are very aware of the corresponding aspects of musical performance. When presented with a new instrument for evaluation, a player will probably
assess its intonation by playing octaves and slow arpeggios over the instrument’s
compass; this is an experimental investigation of its behaviour in the frequency
domain. It is likely that the transient behaviour will be assessed by playing staccato
notes, double-tonguings and trills; this is a typical time domain experiment. The
instrument must not only play in tune, but it must be capable of responding flexibly
to the rapid succession of commands sent to the instrument by the player in a
virtuoso performance (see Sect. 1.2.10).
The picture in Fig. 4.7 showing nodes and antinodes of a standing wave in a
cylindrical tube illustrates one aspect of a frequency domain view of the acoustical
behaviour of the tube. It shows how the tube responds to excitation by a continuous
sinusoidal disturbance at a specific frequency. To complete the frequency domain
picture, it would be necessary to repeat the calculation for many different values of
the frequency.
We have already described a simple but illuminating time domain experiment
which can be carried out on a brass instrument without elaborate scientific equipment. Slapping the palm of the hand on to the open surface of the mouthpiece sends
a pulse down the air column, and a microphone just outside the bell records the
sound radiated by the instrument.
Figure 4.8 was obtained by gently slapping a palm against the mouthpiece rim
on a Conn 8H tenor trombone with the slide in first position. The radiated sound
was recorded using a small lapel microphone whose output was connected to the
external microphone input of a laptop running the free software program Audacity.