Related Experiment Video
Updated: Aug 9, 2026
04:54
A Stable Phantom Material for Optical and Acoustic Imaging
Published on: June 16, 2023
Curle's equation and acoustic scattering by a sphere
Anthony M J Davis1, Raymond J Nagem
1Mathematics Department, University of Alabama, Tuscaloosa, Alabama 35487-0350, USA.
The Journal of the Acoustical Society of America
|April 29, 2006
Summary
This study confirms Curle's equation for acoustic scattering by spheres in inviscid fluids. It also reveals that neglecting viscosity in scattering problems leads to incomplete predictions of far-field pressure.
Area of Science:
- Acoustics
- Fluid Dynamics
- Aeroacoustics
Background:
- Recent research explores connections between aeroacoustic theory and acoustic scattering.
- Acoustic scattering by spheres is a fundamental problem with theoretical and practical implications.
Purpose of the Study:
- To investigate Curle's equation in acoustic scattering by a sphere.
- To analyze the impact of viscosity on acoustic scattering predictions.
- To extend scattering solutions to elastic spheres in viscous fluids.
Main Methods:
- Derivation of Curle's equation for linear acoustic scattering.
- Development of a complete solution for scattering by a rigid sphere in a viscous fluid.
- Extension of the null field solution to include vorticity modes.
- Construction of a solution for an elastic sphere in a viscous fluid.
Main Results:
- Explicit confirmation of Curle's equation for plane wave scattering by a rigid sphere in an inviscid fluid.
- Demonstration that neglecting viscous terms leads to incomplete far-field dipole pressure predictions.
- Recovery of the rigid sphere/null field solution from the elastic sphere solution in a limiting case.
Conclusions:
- Curle's equation is validated for specific inviscid scattering scenarios.
- Viscous effects are crucial for accurate far-field pressure predictions in acoustic scattering.
- The developed framework accommodates both rigid and elastic scatterers in viscous media.
Related Concept Videos
01:22Surface Area Calculations
Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...
01:26Gauss's Law: Spherical Symmetry
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
01:22Electric Field of a Non Uniformly Charged Sphere
Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
01:25Divergence and Curl of Electric Field
The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
01:25Poisson's And Laplace's Equation
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
01:20Gauss's Law: Cylindrical Symmetry
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...