Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Video

Updated: Mar 19, 2026

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
08:49

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions

Published on: February 17, 2019

7.1K

The pulsating orb: solving the wave equation outside a ball.

P A Martin1

  • 1Department of Applied Mathematics and Statistics , Colorado School of Mines , Golden, CO 80401, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|June 10, 2016
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

2.4K
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...
2.4K
The de Broglie Wavelength02:32

The de Broglie Wavelength

34.3K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
34.3K
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

9.7K
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...
9.7K
Wave Parameters01:10

Wave Parameters

9.6K
The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...
9.6K
Equations of Wave Motion01:02

Equations of Wave Motion

8.8K
Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
8.8K
Principle of Angular Impulse and Momentum: Problem Solving01:19

Principle of Angular Impulse and Momentum: Problem Solving

579
Consider a ball of mass m, attached to a massless rod of known length, subjected to a time-dependent torque. If the initial velocity of the mass is known, then the final velocity of the mass for time t can be determined using the principle of angular impulse and momentum.
Initially, a free-body diagram of the system is drawn to illustrate all the forces acting upon the system, providing a crucial understanding of the dynamics at play. Then, the principle of angular impulse and momentum is...
579

You might also read

Related Articles

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

Sort by
Same journal

Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta.

Proceedings. Mathematical, physical, and engineering sciences·2025
Same journal

Inferring the shape of data: a probabilistic framework for analysing experiments in the natural sciences.

Proceedings. Mathematical, physical, and engineering sciences·2023
Same journal

The Elbert range of magnetostrophic convection. I. Linear theory.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Soft wetting with (a)symmetric Shuttleworth effect.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

The quantum theory of time: a calculus for q-numbers.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Integrable nonlinear evolution equations in three spatial dimensions.

Proceedings. Mathematical, physical, and engineering sciences·2022

This study reviews initial-boundary value problems (IBVPs) for acoustic wave equations, focusing on mathematical properties and solutions. It details how Laplace transforms handle wave discontinuities, illustrated with spherical wave examples.

Area of Science:

  • Acoustics and Wave Phenomena
  • Mathematical Physics

Background:

  • Transient acoustic waves arise from object oscillations or scattering, posing initial-boundary value problems (IBVPs) for the wave equation.
  • Understanding wave characteristics, wavefronts, and compatibility conditions is crucial for analyzing these problems.

Approach:

  • This work reviews the formulation and properties of IBVPs, emphasizing weak solutions and continuum mechanics constraints.
  • The Laplace transform method is explored for solving IBVPs, particularly for discontinuous solutions across wavefronts.

Key Points:

  • Basic properties of the wave equation, including characteristics and wavefronts, are discussed.
  • The formulation and properties of IBVPs are reviewed, with a focus on weak solutions.
  • The application of Laplace transforms to IBVPs with discontinuous solutions is detailed.
Keywords:
Laplace transformacousticssound pulsestime domaintransient problemswave equation

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K
Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations
06:51

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Published on: August 21, 2018

7.5K

Related Experiment Videos

Last Updated: Mar 19, 2026

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
08:49

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions

Published on: February 17, 2019

7.1K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K
Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations
06:51

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Published on: August 21, 2018

7.5K

Conclusions:

  • The study provides a comprehensive review of initial-boundary value problems for acoustic waves.
  • Explicit solutions to simple IBVPs for a sphere demonstrate the practical application of the discussed concepts.