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Related Concept Videos

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...
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.
Standing Waves01:17

Standing Waves

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
Simple Harmonic Motion01:21

Simple Harmonic Motion

Simple harmonic motion is the name given to oscillatory motion for a system where the net force can be described by Hooke's law. If the net force can be described by Hooke's law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position. To derive an equation for period and frequency, the equation of motion is used. The period of a simple harmonic oscillator is given...
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:
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to the...

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Related Experiment Video

Updated: Jun 3, 2026

Measurement of Chladni Mode Shapes with an Optical Lever Method
04:39

Measurement of Chladni Mode Shapes with an Optical Lever Method

Published on: June 5, 2020

Vibrational modes in a two-dimensional aperiodic harmonic lattice.

F A B F de Moura1

  • 1Instituto de Física, Universidade Federal de Alagoas, Maceió-AL 57072-970, Brazil.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 16, 2011
PubMed
Summary

We discovered a new phase of extended states in harmonic lattices with varied mass distributions. Increased aperiodicity leads to ballistic energy pulse propagation, revealing novel collective excitation behaviors.

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Area of Science:

  • Condensed matter physics
  • Classical mechanics
  • Solid-state physics

Background:

  • Collective excitations in harmonic lattices are fundamental to understanding wave propagation.
  • Previous studies often focused on periodic or random mass distributions.

Purpose of the Study:

  • Investigate collective excitations in classical harmonic lattices with aperiodic and pseudo-random mass distributions.
  • Characterize the emergence of new phases and energy propagation dynamics.

Main Methods:

  • Matrix recursive reformulation of the mass displacement equation.
  • Numerical computation of localization length.
  • Numerical solution of Hamilton equations for momentum and displacement.

Main Results:

  • A new phase of extended states was identified for aperiodic mass arrays.
  • Ballistic propagation of energy pulses was observed for sufficient aperiodicity.
  • Localization length was computed within the allowed frequency band.

Conclusions:

  • Aperiodic mass distributions in harmonic lattices can lead to extended states, challenging previous assumptions.
  • The observed ballistic energy propagation highlights unique dynamic behaviors in these systems.