Nonlinear progressive waves in a slide trombone resonator

Abstract

The propagation of finite-amplitude waves inside a slide trombone is studied through direct pressure measurements corresponding to dynamic extremes. A two-microphone method is used to separate left-moving and right-moving waves inside the trombone, permitting the detection of nonlinear effects associated with progressive waves. It is found that a redistribution of energy across the spectrum toward the higher-frequencies occurs for large distances and high initial pressure levels. These results are consistent with the theory of weakly nonlinear acoustics and also with those reported in this same context by other authors, but which have been obtained mostly through examination of standing-waves.

A finite volume approach for the simulation of nonlinear dissipative acoustic wave propagation

“…Considering the non-dimensional character of the variables used here, expressions (36), (37) and (38), are consistent with other finite volume methods for Euler equations 34 . A limitation of this method is evidenced by analysis of expressions (32) and (33): eigenvalues can become nonreal.…”

Adaptive calibration of a three-microphone system for acoustic waveguide characterization under time-varying conditions

“…17 Although wave propagation in an instrument bore may become non-linear at high playing levels, 37 this would not invalidate the basic two-microphone wave separation method because such effects are small over short distances, thus allowing for a locally linear approximation. 21 The approach taken in the present study may also lend itself to improvements and extensions in other applications. For example, a more accurate impedance measurement in the presence of a mean flow may be possible if the Mach number is included in the calibration procedure.…”

“…This approach has recently been investigated through theory and simulations by Naucl er and S€ oderstr€ om 20 within the constraints typical of control applications. Another recent study of direct relevance is the investigation into nonlinear wave propagation by Rend on et al 21 in which pulse waves in a trombone are successfully separated using a technique based on the classic two-microphone method. 7 However, none of these methods adapt to the conditions, and in all cases, the estimation accuracy is compromised somewhat by neglecting the propagation losses.…”

Nonlinear sound propagation in two-dimensional curved ducts: a multimodal approach

“…1996; Rendón et al. 2010), or the call of an elephant propagating down its trunk (Gilbert et al. 2014), to the design of automotive exhaust pipes and the curved air intakes on military aircraft (Brambley & Peake 2008), many ducts feature both a complex geometry and pressure waves of sufficient amplitude that nonlinearity should not be ignored.…”

“…Acoustic ducts of different shapes and sizes are ubiquitous in engineering applications as well as everyday life. From the curves and flare in a trombone (Hirschberg et al 1996;Rendón et al 2010), or the call of an elephant propagating down its trunk (Gilbert et al 2014), to the design of automotive exhaust pipes and the curved air intakes on military aircraft (Brambley & Peake 2008), many ducts feature both a complex geometry and pressure waves of sufficient amplitude that nonlinearity should not be ignored. Until now, most work has dealt with either the geometrical problem of curved-duct acoustics in a linear regime or nonlinear acoustics in simple geometries.…”