36
2 The Scientist’s Perspective on Brass Instrument Behaviour
where p tot is the total pressure at some instant, p atmos is the steady atmospheric
pressure that would exist in the absence of a sound wave at that time and p ac is the
pressure change due to the presence of the sound wave. Since p atmos 100,000 Pa
and the peak-peak amplitude of p ac is less than 4 Pa even in the forte part of the note
illustrated in Fig. 2.2, the variations due to acoustic pressure would be too small to be
visible on a plot of total pressure. Frequently in discussion of acoustic phenomena,
acoustic pressure is simply described as pressure; it is usually clear from the context
whether the meaning is intended to be total pressure or acoustic pressure.
The quantity plotted as a function of time in Fig. 2.2b–d is the instantaneous
value of the acoustic pressure p ac (t). In describing the strength of the signal, it is
common to use the root mean square (rms) pressure, defined between two times t 1
and t 2 as
p rms =
t 2
t 1
p ac (t) 2
(t 2 − t 1 )
dt.
(2.3)
The strength of an acoustic signal is often described using the sound pressure
level (SPL) scale. The SPL value L p in decibels (dB) is related to the rms acoustic
pressure by the equation
L p = 20 log 10
p rms
p 0
,
(2.4)
with the reference pressure p 0 = 0.00002 Pa. An increase of p ac by a factor of 10
corresponds to an increase of L p by 20 dB. The relationship between SPL levels in
decibels and the perceived loudness of the sound depends on many factors, including
the frequency content of the sound and the acuity of the listener’s hearing, but
the difference between pianissimo and fortissimo on a brass instrument can reach
around 40 dB.
2.1.2 Sound Measured Inside a Trombone Mouthpiece
Having examined the properties of the sound waves radiated from a brass instrument, the natural next step for the scientist is to investigate the nature of the pressure
changes taking place inside the instrument during the performance. Figure 2.3a
illustrates the signal recorded by a miniature microphone monitoring the acoustic
pressure inside the mouthpiece of the trombone on which the note shown in Fig. 2.2a
was played. At first sight this signal may look similar to the radiated pressure signal
in Fig. 2.2b, but there is in fact a dramatic difference: in this case the pressure scale is
in kPa, and the pressure amplitude in the mouthpiece is several orders of magnitude
2 The Scientist’s Perspective on Brass Instrument Behaviour
where p tot is the total pressure at some instant, p atmos is the steady atmospheric
pressure that would exist in the absence of a sound wave at that time and p ac is the
pressure change due to the presence of the sound wave. Since p atmos 100,000 Pa
and the peak-peak amplitude of p ac is less than 4 Pa even in the forte part of the note
illustrated in Fig. 2.2, the variations due to acoustic pressure would be too small to be
visible on a plot of total pressure. Frequently in discussion of acoustic phenomena,
acoustic pressure is simply described as pressure; it is usually clear from the context
whether the meaning is intended to be total pressure or acoustic pressure.
The quantity plotted as a function of time in Fig. 2.2b–d is the instantaneous
value of the acoustic pressure p ac (t). In describing the strength of the signal, it is
common to use the root mean square (rms) pressure, defined between two times t 1
and t 2 as
p rms =
t 2
t 1
p ac (t) 2
(t 2 − t 1 )
dt.
(2.3)
The strength of an acoustic signal is often described using the sound pressure
level (SPL) scale. The SPL value L p in decibels (dB) is related to the rms acoustic
pressure by the equation
L p = 20 log 10
p rms
p 0
,
(2.4)
with the reference pressure p 0 = 0.00002 Pa. An increase of p ac by a factor of 10
corresponds to an increase of L p by 20 dB. The relationship between SPL levels in
decibels and the perceived loudness of the sound depends on many factors, including
the frequency content of the sound and the acuity of the listener’s hearing, but
the difference between pianissimo and fortissimo on a brass instrument can reach
around 40 dB.
2.1.2 Sound Measured Inside a Trombone Mouthpiece
Having examined the properties of the sound waves radiated from a brass instrument, the natural next step for the scientist is to investigate the nature of the pressure
changes taking place inside the instrument during the performance. Figure 2.3a
illustrates the signal recorded by a miniature microphone monitoring the acoustic
pressure inside the mouthpiece of the trombone on which the note shown in Fig. 2.2a
was played. At first sight this signal may look similar to the radiated pressure signal
in Fig. 2.2b, but there is in fact a dramatic difference: in this case the pressure scale is
in kPa, and the pressure amplitude in the mouthpiece is several orders of magnitude