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Related Concept Videos

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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Wave Parameters01:10

Wave Parameters

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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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Interference and Superposition of Waves01:07

Interference and Superposition of Waves

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When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect of the waves is the sum of the individual waves' effects. However, it does not imply that the individual waves affect the propagation of other waves.
Interference occurs in mechanical waves, such as sound waves, waves on a string, and surface water waves. Mechanical waves correspond to the physical displacement of particles. Hence,...
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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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Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

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A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it. 
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time....
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Propagation of Waves01:07

Propagation of Waves

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When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
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Updated: Feb 17, 2026

Film Control to Study Contributions of Waves to Droplet Impact Dynamics on Thin Flowing Liquid Films
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Film Control to Study Contributions of Waves to Droplet Impact Dynamics on Thin Flowing Liquid Films

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Nonlinear water waves: introduction and overview.

A Constantin1

  • 1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria adrian.constantin@univie.ac.at.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 13, 2017
PubMed
Summary
This summary is machine-generated.

Understanding nonlinear water waves requires advanced methods beyond linear theory. Research highlights interdisciplinary approaches combining analysis, computation, and experiments for large-amplitude wave phenomena.

Keywords:
currentswater flowswaves

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Area of Science:

  • Fluid dynamics
  • Applied mathematics
  • Oceanography

Background:

  • The study of water waves has a long history, with recent advances focusing on large-amplitude waves.
  • Linear theory is insufficient for large-amplitude waves, necessitating nonlinear approaches.
  • Progress relies on discovering structural properties and employing advanced analytical and computational tools.

Discussion:

  • This issue explores nonlinear water waves, reflecting discussions from a 2017 program at the Isaac Newton Institute.
  • The research is interdisciplinary, integrating mathematical analysis, numerical computation, and experimental/field data.
  • New theoretical methodologies, computational approaches, and experimental results are presented.

Key Insights:

  • Nonlinearity is crucial for understanding large-amplitude water waves.
  • Structural properties and creative approaches are key to advancing the field.
  • Interdisciplinary collaboration enhances the study of complex wave phenomena.

Outlook:

  • Continued exploration of nonlinear water wave dynamics is expected.
  • Further integration of theoretical, computational, and experimental methods will drive future research.
  • Discovering underlying structures in wave behavior may reveal unexpected patterns and aesthetic qualities.