2.2 An Approach to Modelling Brass Instruments
59
instrument, that the condition for strong sound generation (efficient reflection back
towards the lips of sound arriving at the bell) is opposed to the condition for strong
sound radiation (efficient transmission into the environment of sound arriving at the
bell).
The resolution of this paradox comes through understanding the way in which
the reflection and transmission of a sound wave at the bell depend on the frequency
of the wave. This topic is discussed in detail in Sect. 4.3. A characteristic feature
of the acoustical behaviour of a flaring bell is that it is very efficient at reflecting
low-frequency waves back into the instrument but very efficient at radiating highfrequency waves into the environment. The frequency above which reflections
become negligible is known as the cutoff frequency of the bell. For a trombone, the
cutoff frequency is typically around 800 Hz. Consider the note B 3 with a repetition
frequency of 233 Hz, which is discussed in Sect. 2.2.3. The fundamental component
of the sound wave is almost completely reflected when it arrives at the bell, giving
a strong feedback to strengthen the lip vibration. The internal sound wave also
contains frequency components which are harmonics of 233 Hz, and the higher
harmonics are radiated with very high efficiency. To summarise, before the sound
wave can radiate (most efficiently by its high harmonics), it must be generated by
the lip vibration (assisted mainly by the low harmonics).
59
instrument, that the condition for strong sound generation (efficient reflection back
towards the lips of sound arriving at the bell) is opposed to the condition for strong
sound radiation (efficient transmission into the environment of sound arriving at the
bell).
The resolution of this paradox comes through understanding the way in which
the reflection and transmission of a sound wave at the bell depend on the frequency
of the wave. This topic is discussed in detail in Sect. 4.3. A characteristic feature
of the acoustical behaviour of a flaring bell is that it is very efficient at reflecting
low-frequency waves back into the instrument but very efficient at radiating highfrequency waves into the environment. The frequency above which reflections
become negligible is known as the cutoff frequency of the bell. For a trombone, the
cutoff frequency is typically around 800 Hz. Consider the note B 3 with a repetition
frequency of 233 Hz, which is discussed in Sect. 2.2.3. The fundamental component
of the sound wave is almost completely reflected when it arrives at the bell, giving
a strong feedback to strengthen the lip vibration. The internal sound wave also
contains frequency components which are harmonics of 233 Hz, and the higher
harmonics are radiated with very high efficiency. To summarise, before the sound
wave can radiate (most efficiently by its high harmonics), it must be generated by
the lip vibration (assisted mainly by the low harmonics).