Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Electric Field of a Non Uniformly Charged Sphere

Electric 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...

Gauss's Law: Spherical Symmetry

Gauss'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...

Electrostatic Boundary Conditions

Electrostatic Boundary Conditions

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...

Boundary Conditions for Current Density

Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.

Magnetostatic Boundary Conditions

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...

Reflection of Waves

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Iterative Born solver for the acoustic Helmholtz equation with heterogeneous sound speed and density.

The Journal of the Acoustical Society of America·2026

Same author

Open letter on intervention regimes and adverse events in focused ultrasound for neuromodulation.

Brain stimulation·2025

Same author

Ultrasound system for precise neuromodulation of human deep brain circuits.

Nature communications·2025

Same author

A comparative study of experimental and simulated ultrasound beam propagation through cranial bones.

Physics in medicine and biology·2024

Same author

Strategies and safety simulations for ultrasonic cervical spinal cord neuromodulation.

Physics in medicine and biology·2024

Same author

Corrigendum to 'Safety Review of Therapeutic Ultrasound for Spinal Cord Neuromodulation and Blood-Spinal Cord Barrier Opening' [Ultrasound in Med & Biol. 50 (2024) 317-331].

Ultrasound in medicine & biology·2024

Search research articles

Related Experiment Video

Updated: Jul 13, 2026

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Acoustic scattering by a sphere with a hemispherically split boundary condition.

Bradley E Treeby¹, Jie Pan, Roshun M Paurobally

¹Centre for Acoustics, Dynamics and Vibration, School of Mechanical Engineering, The University of Western Australia, Crawley, WA, Australia. treebs@mech.uwa.edu.au

The Journal of the Acoustical Society of America

|July 7, 2007

Summary

This study presents a model for sound scattering by a sphere with two impedance hemispheres. It reveals modal cross-coupling influenced by impedance mismatch and source incidence, analogous to combining sectors of uniform spheres.

More Related Videos

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

A Stable Phantom Material for Optical and Acoustic Imaging

A Stable Phantom Material for Optical and Acoustic Imaging

Published on: June 16, 2023

Related Experiment Videos

Last Updated: Jul 13, 2026

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

A Stable Phantom Material for Optical and Acoustic Imaging

A Stable Phantom Material for Optical and Acoustic Imaging

Published on: June 16, 2023

Area of Science:

Acoustics
Wave Scattering
Boundary Value Problems

Background:

Sound scattering by spheres is crucial in acoustics.
Nonuniform boundary conditions present unique challenges in modeling.
Understanding modal coupling is key to predicting scattering behavior.

Purpose of the Study:

To develop a general analytical model for sound scattering by a sphere with a hemispherically divided impedance boundary.
To investigate the modal contributions and cross-coupling phenomena.
To analyze the influence of impedance mismatch and source incidence on scattering characteristics.

Main Methods:

Development of a general analytical model for time-harmonic acoustic pressure.
Analysis of modal contributions and cross-coupling between wave modes.
Simulation of specific cases with varying source incidence and hemispherical impedance values.

Main Results:

Identified modal cross-coupling between incoming and scattered wave modes of unequal degree but opposite parity.
Demonstrated that cross-coupling is strongest between adjacent modes and depends on impedance mismatch.
Showcased scattering characteristics analogous to combining sectors of uniformly bounded spheres.

Conclusions:

The developed analytical model accurately describes sound scattering from a hemispherically divided sphere.
Modal cross-coupling is a significant factor influenced by boundary impedance heterogeneity.
The findings provide insights into acoustic scattering from complex, nonuniform surfaces.