Pressure fields in the vicinity of brass musical instrument bells measured using a two dimensional grid array and comparison with multimodal models

Brass musical instruments act as a source of spherical waves for low frequencies while at higher frequencies the directivity produces a diffracting beam. The directivity and radius of the wavefronts (and therefore the source position) may be expected to depend on the frequency in addition to the geometry of the bell. In this work, experimental determination of the wavefronts propagating from the bell section of brass instruments was performed using a moveable line array of microphones. Exponential sine sweep measurements were performed for each microphone position, effectively giving synchronised impulse responses at every microphone position in a two-dimensional grid starting directly in front of the bell. Calculations were then carried out to check to what extent the observed field was consistent with the predictions from multimodal theory. The multimodal radiation impedance was only known previously for specific geometries such as the infinite baffle, but here an extension of the theory is set out in order to simulate a trombone radiating within a large radius, infinite length cylindrical pipe.