Interactions between Sound Waves

Dean, L. W.

doi:10.1121/1.1918241

Cited by 20 publications

(14 citation statements)

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“…For spherically symmetric interacting waves, our analytic solution is exact and reduces to Baxter's [33] for this special case, where we show that Baxter's solution satisfies the Sommerfeld radiation condition but Dean's [29] does not. Analytic solutions are derived for the second-order field due to the interaction of a plane and spherical wave.…”

Section: Discussionmentioning

confidence: 94%

“…Equation (90) reduces exactly to Baxter's solution [33]. Compared to Baxter's solution, it is found that Dean's earlier solution [29] has an extra term proportional to the spherical Bessel function j 0 (k ± r) so violates the Sommerfeld radiation condition (online supplementary material). A further approximation made by Dean for the far field k ± r 1 and a small object k ± a 1, however, satisfies the Sommerfeld radiation condition because it contains only the dominant e ik±r log(k ± r)/r term.…”

Section: Scattered-scattered Interactionmentioning

confidence: 97%

“…Westervelt later solved the time-harmonic non-collinear planewave case [11] and estimated the second order field of an endfire array so inventing the parametric array [3] which is a wave-wave based instrument with mature and well tested theory [1]. Then Dean and Baxter obtained time-harmonic solutions for the omnidirectional cylindrical [29] and spherical [29,33] wave cases, and Tjotta et al, investigated II interaction for time-harmonic incident beams [40][41][42]. Jones and Beyer measured the second-order acoustic field at the sum frequency caused by an object in the overlap region of two primary incident waves [1,35] and proposed a heuristic formula consistent with an SS-type mechanism based on Dean's solution.…”

Section: Discussionmentioning

confidence: 99%

“…Let p I2 of Equation (23) and the associated second order velocity v I2 due to wave-wave interactions be further decomposed as [29] p I2 (r, t) = p 2 (r, t) + p 2 (r, t) and v I2 (r, t) = − 1…”

Section: General Approachmentioning

confidence: 99%

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Active Nonlinear Acoustic Sensing of an Object with Sum or Difference Frequency Fields

et al. 2017

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A number of nonlinear acoustic sensing methods exist or are being developed for diverse areas ranging from oceanic sensing of ecosystems, gas bubbles, and submerged objects to medical sensing of the human body. Our approach is to use primary frequency incident waves to generate second order nonlinear sum or difference frequency fields that carry information about an object to be sensed. Here we show that in general nonlinear sensing of an object, many complicated and potentially unexpected mechanisms can lead to sum or difference frequency fields. Some may contain desired information about the object, others may not, even when the intention is simply to probe an object by linear scattering of sum and difference frequency incident waves generated by a parametric array. Practical examples illustrating this in ocean, medical, air and solid earth sensing are given. To demonstrate this, a general and complete second-order theory of nonlinear acoustics in the presence of an object is derived and shown to be consistent with experimental measurements. The total second-order field occurs at sum or difference frequencies of the primary fields and naturally breaks into (A) nonlinear waves generated by wave-wave interactions, and (B) second order waves from scattering of incident wave-wave fields, boundary advection, and wave-force-induced centroidal motion. Wave-wave interactions are analytically shown to always dominate the total second-order field at sufficiently large range and carry only primary frequency response information about the object. As range decreases, the dominant mechanism is shown to vary with object size, object composition, and frequencies making it possible for sum or difference frequency response information about the object to be measured from second-order fields in many practical scenarios. It is also shown by analytic proof that there is no scattering of sound by sound outside the region of compact support intersection of finite-duration plane waves at sum or difference frequencies, to second-order. Analytic expressions for second-order fields due to combinations of planar and far-field wave-wave interactions are also derived as are conditions for when wave-wave interactions will dominate the second order field.

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Section: Discussionmentioning

confidence: 94%

Section: Scattered-scattered Interactionmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

Section: General Approachmentioning

confidence: 99%

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Active Nonlinear Acoustic Sensing of an Object with Sum or Difference Frequency Fields

et al. 2017

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“…This configuration creates beams that start to spatially interact very near the transducer surface. These ultrasound waves interact with each other and this phenomenon is known as scattering sound by sound or parametric mixing, which has been explored by Thuras, Westervelt, and others [23-26]. When two sound waves of different frequencies propagate together in a nonlinear medium, additional acoustic waves are produced at harmonics of the two original waves (2 f 1 , 2 f 2 ) as well as at the sum ( f 1 + f 2 ) and difference ( f 1 − f 2 ) frequencies of the two different frequencies [27].…”

Section: Methodsmentioning

confidence: 99%

A beamforming study for implementation of vibro-acoustography with a 1.75-D array transducer

Urban

Chalek

Haider

et al. 2013

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Vibro-acoustography (VA) is an ultrasound-based imaging modality that uses radiation force produced by two cofocused ultrasound beams separated by a small frequency difference, Δf, to vibrate tissue at Δf. An acoustic field is created by the object vibration and measured with a nearby hydrophone. This method has recently been implemented on a clinical ultrasound system using one-dimensional (1D) linear array transducers. In this article, we discuss VA beamforming and image formation using a 1.75D array transducer. A 1.75D array transducer has several rows of elements in the elevation direction which can be controlled independently for focusing. The advantage of the 1.75D array over a 1D linear array transducer is that multiple rows of elements can be used for improving elevation focus for imaging formation. Six configurations for subaperture design for the two ultrasound beams necessary for VA imaging were analyzed. The point-spread functions for these different configurations were evaluated using a numerical simulation model. Four of these configurations were then chosen for experimental evaluation with a needle hydrophone as well as for scanning two phantoms. Images were formed by scanning a urethane breast phantom and an ex vivo human prostate. VA imaging using a 1.75D array transducer offers several advantages over scanning with a linear array transducer including improved image resolution and contrast due to better elevation focusing of the imaging point-spread function.

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References

2016

Hydroacoustic Ocean Exploration

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Interactions between Sound Waves

Cited by 20 publications

References 0 publications

Active Nonlinear Acoustic Sensing of an Object with Sum or Difference Frequency Fields

Active Nonlinear Acoustic Sensing of an Object with Sum or Difference Frequency Fields

A beamforming study for implementation of vibro-acoustography with a 1.75-D array transducer

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