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Travelling Waves01:04

Travelling Waves

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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.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is...
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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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The de Broglie Wavelength02:32

The de Broglie Wavelength

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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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Standing Waves01:17

Standing Waves

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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...
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Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

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The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx  and a shunt capacitance CΔx.
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Wave Parameters01:10

Wave Parameters

9.0K
The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...
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Related Experiment Video

Updated: Jan 15, 2026

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
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Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

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Wavelength Selection for Periodic Travelling Waves: An Unsolved Problem.

Lukas Eigentler1,2, Mattia Sensi3,4

  • 1Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, Coventry, United Kingdom. lukas.eigentler@warwick.ac.uk.

Bulletin of Mathematical Biology
|January 14, 2026
PubMed
Summary

Periodic travelling waves (PTWs) adapt ecosystem patterns by changing wavelength. This study reviews PTW wavelength change prediction and explores selection mechanisms, revealing new trends and potential extinction risks.

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Last Updated: Jan 15, 2026

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • Periodic travelling waves (PTWs) are key to understanding spatio-temporal patterns in biology and ecology.
  • Ecosystems adapt to environmental changes by altering pattern wavelengths, a trait shared by PTW solutions.
  • Existing research focuses on predicting parameter thresholds for PTW wavelength changes, but lacks theory on wavelength selection.

Purpose of the Study:

  • To review methods for predicting PTW wavelength changes using linear stability analysis and Busse balloon theory.
  • To investigate the current theoretical limitations in explaining PTW wavelength selection.
  • To present new numerical findings on PTW wavelength selection during transitions and explore potential extinction dynamics.

Main Methods:

  • Review of linear stability analysis and Busse balloon theory for predicting PTW wavelength changes.
  • Analysis of PTW solutions in λ-ω systems for predator-prey dynamics.
  • Numerical simulations to observe PTW-to-PTW transitions and wavelength selection patterns.

Main Results:

  • Busse balloon theory effectively predicts wavelength change parameters but not selection.
  • New numerical trends show certain stable wavelengths are preferentially selected during transitions.
  • PTW cascades can lead to extinction, even when bistable with PTWs.

Conclusions:

  • There is a significant gap in theoretical understanding of PTW wavelength selection mechanisms.
  • Further research is needed to develop predictive theories for wavelength selection.
  • Exploring new approaches is crucial for deeper insights into PTW dynamics and ecosystem adaptation.