Pablo L. Rendón

Nonlinear progressive waves in a slide trombone resonator

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

Abstract A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional finite volume method using the Roe linearization was implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a High Intensity Focused Ultrasound (HIFU) system, both with satisfactory results. The code, available under an open source license, is written for parallel execution on a Graphics Processing Unit (GPU), thus improving performance by a factor of over 60 when compared to the standard serial execution finite volume code CLAWPACK 4.6.1, which has been used as reference for the implementation logic as well.

A simple method for synthesizing and producing guitar sounds

An uncomplicated model is proposed to describe the transverse force exerted by a plucked string on a guitar bridge. This model incorporates the effect of internal damping, lending the synthesized sound a transient quality that makes it more realistic than sound produced without taking damping into account. The synthesized signals are then compared to actual measurements for both free and palm-muted vibrations, and show agreement in both cases. These synthesized signals can also be used to play MIDI files through a guitar acting as a modified loudspeaker cone, driving the instrument mechanically. The sound thus obtained is realistic and provides an interesting classroom exercise for an undergraduate audience. The main set-up is also affordable as a laboratory activity and for public demonstrations, and has the advantage of being simple to implement and flexible enough to allow different kinds of modification. It is, in fact, reliable enough to use as a tool for the comparison of different guitars driven in the same manner.

The Connection Between Entropy and the Absorption Spectra of Schwarzschild Black Holes for Light and Massless Scalar Fields

We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standard assumption which leads to the eikonal equation, that the wave has zero spatial extent. We find that if these waves have wavelengths larger that the Schwarzschild radius, they are very substantially reflected, fully to numerical accuracy. Interestingly, this critical wavelength approximately coincides with the one derived from entropy considerations of the EM field, and is consistent with well known limit results of scattering in the Schwarzschild metric. The propagation speed is also calculated and seen to differ from the value c, for wavelengths larger than Rs, in the vicinity of Rs. As in all classical wave phenomena, whenever the wavelength is larger or comparable to the physical size of elements in the system, in this case changes in the metric, the zero extent ’particle’ description fails, and the wave nature becomes apparent.

Neural activity related to discrimination and vocal production of consonant and dissonant musical intervals

BACKGROUND Relationships between musical pitches are described as either consonant, when associated with a pleasant and harmonious sensation, or dissonant, when associated with an inharmonious feeling. The accurate singing of musical intervals requires communication between auditory feedback processing and vocal motor control (i.e. audio-vocal integration) to ensure that each note is produced correctly. The objective of this study is to investigate the neural mechanisms through which trained musicians produce consonant and dissonant intervals. METHODOLOGY We utilized 4 musical intervals (specifically, an octave, a major seventh, a fifth, and a tritone) as the main stimuli for auditory discrimination testing, and we used the same interval tasks to assess vocal accuracy in a group of musicians (11 subjects, all female vocal students at conservatory level). The intervals were chosen so as to test for differences in recognition and production of consonant and dissonant intervals, as well as narrow and wide intervals. The subjects were studied using fMRI during performance of the interval tasks; the control condition consisted of passive listening. RESULTS Singing dissonant intervals as opposed to singing consonant intervals led to an increase in activation in several regions, most notably the primary auditory cortex, the primary somatosensory cortex, the amygdala, the left putamen, and the right insula. Singing wide intervals as opposed to singing narrow intervals resulted in the activation of the right anterior insula. Moreover, we also observed a correlation between singing in tune and brain activity in the premotor cortex, and a positive correlation between training and activation of primary somatosensory cortex, primary motor cortex, and premotor cortex during singing. When singing dissonant intervals, a higher degree of training correlated with the right thalamus and the left putamen. CONCLUSIONS/SIGNIFICANCE Our results indicate that singing dissonant intervals requires greater involvement of neural mechanisms associated with integrating external feedback from auditory and sensorimotor systems than singing consonant intervals, and it would then seem likely that dissonant intervals are intoned by adjusting the neural mechanisms used for the production of consonant intervals. Singing wide intervals requires a greater degree of control than singing narrow intervals, as it involves neural mechanisms which again involve the integration of internal and external feedback.

Using Schlieren imaging to estimate the geometry of a shock wave radiated by a trumpet bell

The Schlieren method has been used before to visualize weak shock waves radiated from the open ends of brass instruments, but no attempt has previously been undertaken, however, to measure the geometry of the radiated wavefronts using the Schlieren images. In this paper Schlieren visualization is used to estimate the geometry of the two-dimensional shock wavefronts radiated from the bell of a trumpet at different frequencies. It is observed that the geometry of the shocks does change with frequency, in the expected manner. The propagation speeds of these shocks are also calculated, and they too exhibit the anticipated behavior.

A three-dimensional simulation of vortex formation at the open end of an acoustic waveguide

For high enough levels of acoustic pressure inside a tube, a nonlinear mechanism is responsible for the formation of annular vortices at the open end of the tube, which results in energy loss. Higher sound pressure levels in the tube lead in turn to larger values of the acoustic velocity at the exit, and thus to higher Reynolds numbers. It has been observed [Buick et al., 2011] that two regimes are possible depending on whether the acoustic velocity is low, in which case vorticity appears in the immediate vicinity of the tube, or high, in which case vortices are formed at the open end of the tube and are advected outwards. We use a Lattice Boltzmann Method (LBM) to simulate the velocity field at the exit of the tube in 3D, for both cases. We plan to compare these numerical results with experimental results obtained through particle image velocimetry (PIV). The effect of varying both the geometry of the tube and the shape of the termination on the magnitude of the nonlinear losses at the exit is also examined.

Comparison between acoustic measurements of brass instruments and one-dimensional models with curved wavefronts and transformed axial coordinates

A progressive spherical or spheroidal wavefront approximation has previously been found to be a necessary step for a more accurate application of Websters wave equation to rapidly flaring horns. This leads to a necessary transformation of the horn area function, from the usual flat cross-sectional area in terms of the axial coordinate, into a curved cap-like wavefront area as a function of either the axial coordinate, the arc-length coordinate along the horn profile, the leading curved wavefront coordinate, or still other possible longitudinal coordinates. In this article, horn functions, and related frequency potential functions are calculated from the measured horn profiles of a trombone and a trumpet for several of the above parameterizations. From them, cutoff frequencies and effective lengths are determined. A comparison is drawn between theoretical results using different parameterizations, results calculated via transfer-matrix models, and experimental measurements of the acoustical input impedance and reflection function of both instruments. Results indicate that one-dimensional models accurately predict the effective lengths, and consequently the fundamental resonance frequency of the instruments within ±25 cents, but fail noticeably in predicting cutoff frequencies, leading to what is probably an inaccurate representation of perceived timbre.

Numerical study of nonlinear distortion of resonant states in acoustic tubes

A numerical study of nonlinear acoustic propagation inside tubes is presented. Thermoviscous attenuation is included, giving rise to wall losses associated with the boundary layer. The full-wave simulation is performed in the time domain, over a 2D spatial domain assuming axial symmetry, and it is based on a previously validated open source code, using Finite Volume Method implemented in GPU (FiVoNAGI) [Velasco & Rendon, A finite volume approach for the simulation of nonlinear dissipative acoustic wave propagation, 2015]. One intended application is the identification of resonance frequency shifts in the nonlinear regime in brass musical instruments as a function of bore profile and amplitude of the driving stimulus. To gain insight on the nonlinear processes taking place inside the tube, visualizations are presented, differentiating spectral components and traveling waves in both directions.

fMRI Mapping of Brain Activity Associated with the Vocal Production of Consonant and Dissonant Intervals

The neural correlates of consonance and dissonance perception have been widely studied, but not the neural correlates of consonance and dissonance production. The most straightforward manner of musical production is singing, but, from an imaging perspective, it still presents more challenges than listening because it involves motor activity. The accurate singing of musical intervals requires integration between auditory feedback processing and vocal motor control in order to correctly produce each note. This protocol presents a method that permits the monitoring of neural activations associated with the vocal production of consonant and dissonant intervals. Four musical intervals, two consonant and two dissonant, are used as stimuli, both for an auditory discrimination test and a task that involves first listening to and then reproducing given intervals. Participants, all female vocal students at the conservatory level, were studied using functional Magnetic Resonance Imaging (fMRI) during the performance of the singing task, with the listening task serving as a control condition. In this manner, the activity of both the motor and auditory systems was observed, and a measure of vocal accuracy during the singing task was also obtained. Thus, the protocol can also be used to track activations associated with singing different types of intervals or with singing the required notes more accurately. The results indicate that singing dissonant intervals requires greater participation of the neural mechanisms responsible for the integration of external feedback from the auditory and sensorimotor systems than does singing consonant intervals.