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Propagation of Waves01:07

Propagation of Waves

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When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
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Standing Waves in a Cavity01:28

Standing Waves in a Cavity

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A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
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Propagation Speed of Electromagnetic Waves01:30

Propagation Speed of Electromagnetic Waves

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Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:
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Plane Electromagnetic Waves I01:30

Plane Electromagnetic Waves I

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The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...
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Travelling Waves01:04

Travelling Waves

6.6K
A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is...
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Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

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The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx  and a shunt capacitance CΔx.
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Related Experiment Video

Updated: Dec 24, 2025

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

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Wave Propagation on Microstate Geometries.

Joe Keir1

  • 1Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter (550) Woodstock Road, Oxford, OX2 6GG UK.

Annales Henri Poincare
|April 10, 2020
PubMed
Summary

Supersymmetric microstate geometries are proven to have stable wave solutions, avoiding ergosphere instability. Mathematical analysis reveals bounded local energy and sublogarithmic decay rates for wave equations on these backgrounds.

Area of Science:

  • Theoretical Physics
  • String Theory
  • Mathematical Physics

Background:

  • Supersymmetric microstate geometries are conjectured to be unstable.
  • This conjecture is based on numerical and heuristic evidence of slow wave decay.
  • Previous studies suggested potential nonlinear instabilities.

Purpose of the Study:

  • To mathematically analyze the linear wave equation on supersymmetric microstate geometries.
  • To rigorously investigate the stability of these geometries under wave perturbations.
  • To resolve the conjectured instability and understand wave behavior.

Main Methods:

  • Thorough mathematical treatment of the linear wave equation.
  • Analysis on both two- and three-charge microstate geometries.

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  • Construction of quasimodes to bound decay rates.
  • Main Results:

    • Wave solutions exhibit uniformly bounded local energy in both two- and three-charge cases.
    • Three-charge microstates avoid 'ergosphere instability' despite possessing an ergoregion.
    • Sublogarithmic decay rates for wave solutions were found, confirming prior numerical results.

    Conclusions:

    • Supersymmetric microstate geometries are stable with respect to the linear wave equation.
    • The conjectured nonlinear instability is not supported by this linear analysis.
    • Wave dynamics on these backgrounds are characterized by bounded energy and slow decay.