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Trombone Transfer Functions: Comparison Between Frequency-Swept Sine Wave and Human Performer Input

Beauchamp J. W.

Archives of Acoustics

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2012

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Vol. 37, No. 4

447-454

EN

Source/filter models have frequently been used to model sound production of the vocal apparatus and musical instruments. Beginning in 1968, in an effort to measure the transfer function (i.e., transmission response or filter characteristic) of a trombone while being played by expert musicians, sound pressure signals from the mouthpiece and the trombone bell output were recorded in an anechoic room and then subjected to harmonic spectrum analysis. Output/input ratios of the signals’ harmonic amplitudes plotted vs. harmonic frequency then became points on the trombone’s transfer function. The first such recordings were made on analog 1/4 inch stereo magnetic tape. In 2000 digital recordings of trombone mouthpiece and anechoic output signals were made that provide a more accurate measurement of the trombone filter characteristic. Results show that the filter is a high-pass type with a cutoff frequency around 1000 Hz. Whereas the characteristic below cutoff is quite stable, above cutoff it is extremely variable, depending on level. In addition, measurements made using a swept-sine-wave system in 1972 verified the high-pass behavior, but they also showed a series of resonances whose minima correspond to the harmonic frequencies which occur under performance conditions. For frequencies below cutoff the two types of measurements corresponded well, but above cutoff there was a considerable difference. The general effect is that output harmonics above cutoff are greater than would be expected from linear filter theory, and this effect becomes stronger as input pressure increases. In the 1990s and early 2000s this nonlinear effect was verified by theory and measurements which showed that nonlinear propagation takes place in the trombone, causing a wave steepening effect at high amplitudes, thus increasing the relative strengths of the upper harmonics.

2

Nonlinearly coded signals for harmonic imaging

Nowicki A., Wójcik J., Kujawska T.

Archives of Acoustics

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2009

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Vol. 34, No. 1

63-74

EN

In this paper a new method utilizing nonlinear properties of tissues to improve contrast-to-noise ratio is presented. In our novel method the focused circular transducer is excited with two-tone bursts (including the 2.2MHz fundamental and 4.4MHz second harmonic frequencies) with specially coded polarization of each tone. This new approach was named Multitone Nonlinear Coding (MNC) because the choice of both tones polarization and amplitude law, allowing optimization of the probe receiving properties, depends on nonlinear properties of tissue. The numerical simulations of nonlinear fields in water and in tissue-like medium with absorption coefficient of 7Np/(m MHz) are performed. The comparison between the proposed method and the Pulse Inverse (PI) method is presented. The concept of the virtual fields was introduced to explain properties of both the Pulse Inversion and MNC methods and to compare their abilities. It was shown that for the same on-source pressure an application of the MNC method allows to decrease the mechanical index about 40%, to improve lateral resolution from 10 to 30% and to gain the signal-to-noise ratio up to 8 times with respect to the PI method.

3

Computing and measuring nonlinear and linear propagation by two independent methods

Filipczyński L., Kujawska T., Secomski W., Tymkiewicz R., Wójcik J.

Archives of Acoustics

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1999

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Vol. 24, no. 3

269-288

EN

Nonlinear effects, caused by propagation of ultrasonic pulses with finite amplitudes, were computed and measured in water in the case of pulses with pressures up to 1.5MPapp used in diagnostic devices. An electronic transmitter generated high (280Vpp) and low (47Vpp) voltages, applied to a plane PZT transducer causing in this way nonlinear and linear propagation effects. The carrier frequency of the pulse was 2MHz, while its time duration was 2.5\,ms. The measurements were carried out by means of a typical calibrated PVDF membrane hydrophone and by an electromagnetic (EM) hydrophone, prepared for this study. The pulse measurements by means of the PVDF hydrophone showed a higher number of spectral components than those by means of the EM hydrophone. This effect was explained by sensitivity characteristics that increased in the PVDF and decreased in the EM hydrophone as a function of frequency. Previously, it was shown that the effective frequency band used in measurements by means of the PVDF hydrophone is situated below the resonance, on the increasing slope of the resonanse curve. The properties of the EM hydrophone were analysed on the basis of the plane wave assumption. A procedure was developed to correct distortions of the pulse spectrum and its pressure measured by PVDF and EM hydrophones. In the first case the maximum peak-to-peak pulse pressure should be decreased by 27%, while in the second case it should be increased by only 0.7%, and by 3% if an additional amplifier was used. The sensitivities of PVDF and EM hydrohones were very different and equal for the frequency of 2MHz to 28mV/MPa and 0.10mV/MPa, respectively. The calibration of the EM hydrophone was carried out by means of only two simple: electrical and magnetic independent measurements, although in the EM hydrophone there occured external interferring signals. For the theoretic-numerical detemination of the acoustic fields and their spectra generated in the case of nonlinear and linear propagation the numerical procedure called the WJ Code was applied. It was developed recently by the last-named author of this paper. In calculations absorption in water was taken into account. The critical distance, where distortions caused by nonlinear propagation in water were maximum, was determined by a number of computations of the ultrasonic field as a function of the distance from the transducer. A good agreement between computed results and those measured by two different methods, showing the pulse pressure distribution along the whole beam axis, was confirmed. In this case it was shown that the ?/4 matching layer covering the transducer surface influenced the edge wave radiated by the transducer.