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Related Concept Videos

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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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...
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Modes of Standing Waves: II01:04

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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.
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Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
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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.
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Related Experiment Video

Updated: Mar 19, 2026

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
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Lamb-type waves generated by a cylindrical bubble oscillating between two planar elastic walls.

A A Doinikov1, F Mekki-Berrada1, P Thibault1

  • 1CNRS and Université Grenoble-Alpes, LIPhy UMR 5588 , Université Grenoble-Alpes , Grenoble, F-38401, France.

Proceedings. Mathematical, Physical, and Engineering Sciences
|June 9, 2016
PubMed
Summary

The study investigates bubble oscillations in microfluidic channels with elastic walls, revealing novel Lamb-type surface waves. These waves significantly increase bubble resonance frequency compared to rigid walls.

Keywords:
bubblemicrofluidicssolid–fluid interfacesurface waveultrasound

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Area of Science:

  • Fluid dynamics
  • Acoustics
  • Materials science

Background:

  • Microfluidic devices are increasingly used in various scientific applications.
  • Understanding bubble dynamics in confined spaces is crucial for many processes.
  • The behavior of bubbles in channels with elastic walls is not fully understood.

Purpose of the Study:

  • To investigate the volume oscillation of a cylindrical bubble in a microfluidic channel with planar elastic walls.
  • To theoretically describe novel Lamb-type surface waves at fluid-solid interfaces.
  • To analyze the effect of these surface waves on bubble dynamics and resonance frequency.

Main Methods:

  • Analytical solutions for bulk scattered waves and Lamb-type surface waves.
  • Derivation of a dispersion equation for Lamb-type waves.
  • Use of Hankel transforms to solve for wave fields in elastic walls and fluid.
  • Numerical simulations to study bubble dynamics in elastic channels.

Main Results:

  • Novel Lamb-type surface waves propagating at fluid-solid interfaces were theoretically described.
  • A dispersion equation for Lamb-type waves was derived, showing speed dependence on channel height (h) and transverse wave wavelength (λt).
  • Bubble resonance frequency in elastic channels can be up to 50% higher than in rigid channels due to surface wave effects.

Conclusions:

  • Lamb-type surface waves significantly influence bubble dynamics in microfluidic channels with elastic walls.
  • The theoretical framework provides a means to predict wave speed and understand bubble behavior.
  • This research offers insights for designing microfluidic devices with enhanced control over bubble oscillations.