Study of the optimal active control of a trombone

Abstract

In the brass instrument family, the sound can be modified or attenuated using a mute, which is usually inserted in the bell of the instrument. The objective of this paper is to study the principle and the technological feasibility of an active mute using loudspeakers placed in front or around the instrument bell. This mute must reduce the acoustic power emitted by the instrument while avoiding any impact on its playability. At this stage, an optimal control is considered and no real-time controller is implemented. Results show that an active control placed outside the trombone is theoretically feasible and can be efficient to reduce the acoustic power up to 2000 Hz by placing a ring of sources around the bell and a source in front of the trombone. The instrument input impedance is very slightly affected by the control. In accordance with numerical simulations, the experiment showed that placing a control speaker very close in front of the bell of the instrument modifies the pressure field of the instrument in such a way that it allows to obtain a power attenuation greater than the predicted one. The control is technologically achievable but requires a high power for the closest source.

Study of an active mute for controlling the directivity of a trombone

“…The optimal secondary volume flow q opt s is obtained by differentiating the quadratic function of equation 4 with respect to q s [2,6] and generates a unique solution given by:…”

“…M = 614 observation points (∆θ = ∆ϕ = 10 • ) are used to estimate the optimal volume velocity q opt s . This configuration is inspired from a previous work dealing with the control of acoustic power [2] Figures 3 and 4 show the target directivities and the directivities obtained after control respectively at 200 Hz and 1000 Hz. The target cardioid directivity is reached at 200 Hz but not at 1 kHz, the number of control sources being too small.…”

“…In a real application case (trombone), the voltage applied to control loudspeakers depends on the trombone volume velocity spectrum with q p ≃ 1 litre/s at 50 Hz, q p ≃ 5 litre/s at 500 Hz [2] and on the loudspeaker characteristics. The main constraints concerns the control source 1 (z f = 0.05 m) at 50 Hz.…”

“…In order to minimize the acoustic power, different mutes are used by musicians, but they are known to alter the interaction between the instrument and the musician, making it more difficult to play certain notes. Some researchers have proposed either modifying an existing mute by adding an active control system inside the mute [1], or adding speakers near the bell to reduce acoustic power [2]. In the latter case, the proposed system consists of 8 loudspeakers placed around the bell of the trombone and 1 loudspeaker placed on axis in front of the bell.…”