A Note on Finite Difference Estimation of Acoustic Particle Velocity

Jacobsen, Finn

doi:10.1006/jsvi.2002.5023

Cited by 24 publications

(12 citation statements)

References 14 publications

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“…To obtain measurements over the broad frequency range examined here, we use three different experimental setups, each designed to cover a portion of the frequency range. The fluctuating airflow from 100 Hz to 50 kHz near the silk is determined using a measure of the spatial gradient of the pressure, ∂p(x, t)/∂x (36). Knowing the sound-pressure gradient, the acoustic particle velocity v a (x, t) is calculated using Euler's equation: −∂p(x, t)/∂x = ρ 0 ∂v a (x, t)/∂t, where ρ 0 is the air density.…”

Section: Methodsmentioning

confidence: 99%

Sensing fluctuating airflow with spider silk

Zhou

Miles

2017

Proc. Natl. Acad. Sci. U.S.A.

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The ultimate aim of flow sensing is to represent the perturbations of the medium perfectly. Hundreds of millions of years of evolution resulted in hair-based flow sensors in terrestrial arthropods that stand out among the most sensitive biological sensors known, even better than photoreceptors which can detect a single photon (10 −18 -10 −19 J) of visible light. These tiny sensory hairs can move with a velocity close to that of the surrounding air at frequencies near their mechanical resonance, despite the low viscosity and low density of air. No man-made technology to date demonstrates comparable efficiency. Here we show that nanodimensional spider silk captures fluctuating airflow with maximum physical efficiency (V silk /V air ∼ 1) from 1 Hz to 50 kHz, providing an effective means for miniaturized flow sensing. Our mathematical model shows excellent agreement with experimental results for silk with various diameters: 500 nm, 1.6 μm, and 3 μm. When a fiber is sufficiently thin, it can move with the medium flow perfectly due to the domination of forces applied to it by the medium over those associated with its mechanical properties. These results suggest that the aerodynamic property of silk can provide an airborne acoustic signal to a spider directly, in addition to the wellknown substrate-borne information. By modifying a spider silk to be conductive and transducing its motion using electromagnetic induction, we demonstrate a miniature, directional, broadband, passive, low-cost approach to detect airflow with full fidelity over a frequency bandwidth that easily spans the full range of human hearing, as well as that of many other mammals.spider silk | airborne motion | flow sensing | acoustics | nanodimensional fiber M iniaturized flow sensing with high spatial and temporal resolution is crucial for numerous applications, such as high-resolution flow mapping (1), controlled microfluidic systems (2), unmanned microaerial vehicles (3-5), boundary-layer flow measurement (6), low-frequency sound-source localization (7), and directional hearing aids (8). It has important socioeconomic impacts involved with defense and civilian tasks, biomedical and healthcare, energy saving and noise reduction of aircraft, natural and man-made hazard monitoring and warning, etc (1-10). Traditional flow-sensing approaches such as laser Doppler velocimetry, particle image velocimetry, and hot-wire anemometry have demonstrated significant success in certain applications. However, their applicability in a small space is often limited by their large size, high power consumption, limited bandwidth, high interaction with medium flow, and/or complex setups. There are many examples of sensory hairs in nature that sense fluctuating flow by deflecting in a direction perpendicular to their long axis due to forces applied by the surrounding medium (11-16). The simple, efficient, and tiny natural hair-based flow sensors provide an inspiration to address these difficulties. Miniature artificial flow sensors based on various transduction appr...

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Section: Methodsmentioning

confidence: 99%

Sensing fluctuating airflow with spider silk

Zhou

Miles

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…The occurrence of negative active acoustic power in Figure 13, can possibly be explained by amplitude and phase errors caused by the aforementioned diffraction between 4and 6kHz of the probe. Jacobsen [27] found that measurement of the active acoustic intensity in reactive sound fields is very sensitive to such errors.…”

Section: Microphone (8x) Spacermentioning

confidence: 99%

Measuring Sound Absorption: Considerations on the Measurement of the Active Acoustic Power

Kuipers¹,

Wijnant²,

Boer³

2014

Acta Acustica united with Acustica

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SummaryUsing alocal plane wave assumption, one can determine the normal incidence sound absorption coefficient of a surface by measuring the acoustic pressure and the particle velocity normal to that surface. As the measurement surface lies in front of the material surface, the measured active and incident acoustic power will generally deviate from those at the material surface, leading to ap ossibly inaccurate sound absorption coefficient. This phenomenon is particularly pronounced for poorly absorbing surfaces if sound is not normally incident overthe whole material surface. Based on an analytical model, it is shown that the accuracycan be improvedbyextending the measurement surface upon which the active acoustic power is measured. Experimental results demonstrate the usefulness of this approach, in particular for poorly absorbing surfaces.

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“…6 However, until recently measurement of the total sound energy density has required an elaborate arrangement based on finite-difference approximations using at least four pressure microphones. [6][7][8][9] The microphones should be amplitude and phase matched very well, and the signal-to-noise ratio is poor because the finitedifference signals should be time integrated, 10 which is perhaps one of the reasons why the method has not been used much in practice. With the advent of a three-dimensional particle velocity transducer, "Microflown," 11 it has become somewhat easier to measure kinetic and total rather than only potential energy density in a sound field, as demonstrated a few years ago.…”

Section: 2mentioning

confidence: 99%

Statistical properties of kinetic and total energy densities in reverberant spaces

Jacobsen

Molares

2010

The Journal of the Acoustical Society of America

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Many acoustical measurements, e.g., measurement of sound power and transmission loss, rely on determining the total sound energy in a reverberation room. The total energy is usually approximated by measuring the mean-square pressure ͑i.e., the potential energy density͒ at a number of discrete positions. The idea of measuring the total energy density instead of the potential energy density on the assumption that the former quantity varies less with position than the latter goes back to the 1930s. However, the phenomenon was not analyzed until the late 1970s and then only for the region of high modal overlap, and this analysis has never been published. Moreover, until fairly recently, measurement of the total sound energy density required an elaborate experimental arrangement based on finite-difference approximations using at least four amplitude and phase matched pressure microphones. With the advent of a three-dimensional particle velocity transducer, it has become somewhat easier to measure total rather than only potential energy density in a sound field. This paper examines the ensemble statistics of kinetic and total sound energy densities in reverberant enclosures theoretically, experimentally, and numerically.

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A Note on Finite Difference Estimation of Acoustic Particle Velocity

Cited by 24 publications

References 14 publications

Sensing fluctuating airflow with spider silk

Sensing fluctuating airflow with spider silk

Measuring Sound Absorption: Considerations on the Measurement of the Active Acoustic Power

Statistical properties of kinetic and total energy densities in reverberant spaces

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