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Related Concept Videos

Modes of Standing Waves: II01:04

Modes of Standing Waves: II

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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.
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....
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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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Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
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Related Experiment Video

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Measurement of Chladni Mode Shapes with an Optical Lever Method
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Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics.

Yongxian Wang1, Houwang Tu1, Wei Liu1

  • 1College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China.

Entropy (Basel, Switzerland)
|July 2, 2021
PubMed
Summary

Two new spectral methods, Chebyshev-Tau and Chebyshev-Collocation, efficiently compute atmospheric acoustic normal modes. These methods are faster than previous approaches for modeling sound propagation.

Keywords:
Chebyshev polynomialcollocation methodcomputational atmospheric acousticsnormal modestau method

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Area of Science:

  • Computational atmospheric acoustics
  • Acoustic wave propagation modeling

Background:

  • The normal mode model is crucial for calculating atmospheric acoustic fields from single-frequency sound sources.
  • Existing methods often involve complex calculations for modal wavenumbers.

Purpose of the Study:

  • To introduce and develop Chebyshev-Tau and Chebyshev-Collocation spectral methods for solving atmospheric acoustic normal modes.
  • To provide a more efficient computational approach compared to existing methods.

Main Methods:

  • Projecting the governing equation onto orthogonal bases to transform the problem into a dense matrix eigenvalue problem.
  • Utilizing linear algebra methods to solve for eigenvalues and eigenvectors.
  • Developing corresponding computational programs for the spectral methods.

Main Results:

  • The Chebyshev-Tau and Chebyshev-Collocation methods successfully determine modal wavenumbers and modes.
  • Numerical experiments validated the effectiveness of both methods under downwind and upwind conditions.
  • Both proposed spectral methods demonstrated superior speed compared to the Legendre-Galerkin spectral method.

Conclusions:

  • The Chebyshev-Tau and Chebyshev-Collocation methods offer an efficient and effective solution for computing atmospheric acoustic normal modes.
  • These spectral methods provide a faster alternative for acoustic field computations in the atmosphere.