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Related Concept Videos

Modes of Standing Waves: II01:04

Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.
Modes of Standing Waves - I01:03

Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This phenomenon...
Standing Waves in a Cavity01:28

Standing Waves in a Cavity

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:
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...
Magnetostatic Boundary Conditions01:28

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...
Boundary Layer Characteristics01:18

Boundary Layer Characteristics

When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...

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Related Experiment Video

Updated: Jul 2, 2026

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

Eigenmode structure in solar-wind Langmuir waves.

R E Ergun1, D M Malaspina, Iver H Cairns

  • 1Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA.

Physical Review Letters
|September 4, 2008
PubMed
Summary
This summary is machine-generated.

Intense solar-wind Langmuir waves are confirmed as trapped eigenmodes in density wells. This finding is crucial for understanding the origins of solar radio bursts.

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

Last Updated: Jul 2, 2026

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

Building Langmuir Probes and Emissive Probes for Plasma Potential Measurements in Low Pressure, Low Temperature Plasmas
08:10

Building Langmuir Probes and Emissive Probes for Plasma Potential Measurements in Low Pressure, Low Temperature Plasmas

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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

Area of Science:

  • Space Physics
  • Plasma Physics
  • Solar Physics

Background:

  • Intense solar-wind Langmuir waves exhibit complex spatial and frequency signatures.
  • Understanding these waves is key to explaining phenomena like solar radio bursts.
  • Previous studies have lacked direct observational evidence of specific wave structures.

Purpose of the Study:

  • To identify and confirm the nature of observed solar-wind Langmuir wave signatures.
  • To investigate the role of density structures in wave propagation and trapping.
  • To establish a link between linear wave theory and nonlinear phenomena in the solar wind.

Main Methods:

  • Comparing observational data of solar-wind electric field spectra and waveforms with theoretical models.
  • Utilizing 1D linear solutions to analyze wave behavior.
  • Identifying wave patterns consistent with eigenmodes trapped in density wells.

Main Results:

  • Observed spatial and frequency signatures of intense solar-wind Langmuir waves match eigenmodes trapped in parabolic density wells.
  • Measured electric field data can be represented by 1-3 low-order eigenstates.
  • This study provides the first observational confirmation of Langmuir eigenmodes in a space environment.

Conclusions:

  • Linear Langmuir eigenmodes trapped in density wells are a fundamental component of intense solar-wind wave activity.
  • These eigenmodes likely serve as the initial stage for nonlinear processes.
  • The findings are critical for understanding the generation mechanisms of solar type II and type III radio bursts.