Difference-frequency generation in nonlinear scattering of acoustic waves by a rigid sphere

Silva, Glauber T.; Bandeira, Anderson

doi:10.1016/j.ultras.2012.08.015

Cited by 16 publications

(5 citation statements)

References 39 publications

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“…To treat the case of a movable object, we define a complete and self-consistent second order acoustic wave-exciting force, and find previous helpful formulations [28,[45][46][47] missed the effects of some second order field components and overcounted others. (An analytic solution for the SS field arising from a rigid immovable sphere was dervied by Silva and Bandeira [48].) Approximate analytic solutions for the second order nonlinear wave fields found in the presence of low-impedance contrast inhomogeneities, that apply to one or many inhomogeneities, are also derived in Appendix A.…”

Section: Discussionmentioning

confidence: 99%

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: 99%

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

et al. 2017

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“…Because the ultrasound level generated by a PAL is limited, the nonlinearity is weak and the quasilinear approximation can be assumed. 1 After using the method of successive approximations, 28 Eq. ( 5) is decomposed into two coupled linear equations under the harmonic excitation a 22 22 aa 0, 1, 2…”

Section: A Near Fieldmentioning

confidence: 99%

The near field, Westervelt far field, and inverse-law far field of the audio sound generated by parametric array loudspeakers

Zhong

Kirby

Qiu

2021

The Journal of the Acoustical Society of America

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The near and far fields of traditional loudspeakers are differentiated by whether the sound pressure amplitude is inversely proportional to the propagating distance. However, the audio sound field generated by a parametric array loudspeaker (PAL) is more complicated, and in this article it is proposed to be divided into 3 regions: near field, Westervelt far field, and inverselaw far field. In the near field, the audio sound experiences strong local effects and an efficient quasilinear solution is presented. In the Westervelt far field, local effects are negligible so that the Westervelt equation is used, and in the inverse-law far field a simpler solution is adopted. It is found that the boundary between the near and Westervelt far fields for audio sound lies at approximately a 2 /λ -λ/4, where a is transducer radius and λ is ultrasonic wavelength. At large transducer radii and high ultrasonic frequencies, the boundary moves close to the PAL and can be estimated by a closed-form formula. The inverse-law holds for audio sound in the inverselaw far field and is more than 10 meters away from the PAL in most cases. With the proposed classification, it is convenient to apply appropriate prediction models to different regions.

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“…the mechanical properties. Various studies have been conducted on VA, [12][13][14][15][16][17][18] mainly for application to biomedical imaging, such as the detection of lesions and calcifications in soft tissues. Elastography, [19][20][21] like strain elastography and shear wave elastography, is a type of VA method.…”

Section: Introductionmentioning

confidence: 99%

Feasibility of nondestructive testing using transient vibrations excited by acoustic radiation force

Kitamura¹,

Nomura²

2023

Jpn. J. Appl. Phys.

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The use of the transient response in vibro-acoustography to image the mechanical properties of objects was investigated. Verification of the proposed method using aluminum foil showed that transient vibrations are generated by a step-function acoustic radiation force exerted on an object. These vibrations can be used to obtain the frequency characteristics of the object. The proposed method was applied to the one-dimensional imaging of aluminum foil with various mechanical properties. This method captured the distributions of the vibrational amplitude and mode frequencies, which vary according to local mechanical properties. These results show that the proposed method effectively visualizes the mechanical properties of objects.

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Difference-frequency generation in nonlinear scattering of acoustic waves by a rigid sphere

Cited by 16 publications

References 39 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

The near field, Westervelt far field, and inverse-law far field of the audio sound generated by parametric array loudspeakers

Feasibility of nondestructive testing using transient vibrations excited by acoustic radiation force

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