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Related Concept Videos

Modes of Standing Waves - I01:03

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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...
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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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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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Electromagnetic waves can be reflected; the surface of a conductor or a dielectric can act as a reflector. As electric and magnetic fields obey the superposition principle, so do electromagnetic waves. The superposition of an incident wave and a reflected electromagnetic wave produces a standing wave analogous to the standing waves created on a stretched string.
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Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
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Updated: Jun 22, 2025

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
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Nonlinear standing waves for assessing material nonlinearity in thin samples.

Seungo Baek1, Gun Kim1, Jin-Yeon Kim2

  • 1Department of Civil, Urban, Earth, and Environmental Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulju-gun, Ulsan 44919, Republic of Korea.

Ultrasonics
|June 27, 2024
PubMed
Summary

A new acoustic nonlinearity parameter (β) measurement using nonlinear standing waves accurately assesses material damage in thin samples. This advanced second harmonic generation technique overcomes limitations of previous methods for construction materials.

Keywords:
Acoustic nonlinearity parameterMaterial characterizationNonlinear standing wavesSecond harmonic generationWave propagation

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Area of Science:

  • Materials Science
  • Non-Destructive Testing
  • Acoustic Nonlinearity

Background:

  • The acoustic nonlinearity parameter (β) quantifies material nonlinearity using second harmonic generation (SHG).
  • Current SHG methods for measuring β in construction materials are limited by sample size, causing boundary reflections that impede accurate assessment.
  • Large sample requirements restrict the integration of SHG with other material characterization techniques.

Purpose of the Study:

  • To develop a novel SHG method for accurate β measurement in thin material samples.
  • To overcome the limitations of existing SHG techniques related to sample size and boundary reflections.
  • To enable the use of SHG with other characterization modalities for comprehensive material analysis.

Main Methods:

  • A new SHG method utilizing nonlinear standing waves in a forced-free configuration was developed.
  • Corrections for phase delay and attenuation effects of reflected waves were implemented.
  • The method allows for accurate β measurements in thin samples without a thickness-wavelength ratio constraint.

Main Results:

  • The proposed SHG method successfully measured the acoustic nonlinearity parameter (β) in thin samples.
  • Microstructural modifications in cement paste due to thermal damage were quantified using the measured β.
  • The method demonstrated its capability to accurately assess material nonlinearity in constrained sample sizes.

Conclusions:

  • The novel SHG method based on nonlinear standing waves provides accurate β measurements in thin samples.
  • This technique overcomes previous limitations, enabling SHG application in diverse material characterization scenarios.
  • The method is a promising tool for quantifying microstructural changes, such as thermal damage, in materials.