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Related Concept Videos

Wave Parameters01:10

Wave Parameters

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...
Travelling Waves01:04

Travelling Waves

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 water;...
Propagation of Waves01:07

Propagation of Waves

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...
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...
Sound Waves01:01

Sound Waves

Sound waves can be thought of as fluctuations in the pressure of a medium through which they propagate. Since the pressure also makes the medium's particles vibrate along its direction of motion, the waves can be modeled as the displacement of the medium's particles from their mean position.
Sound waves are longitudinal in most fluids because fluids cannot sustain any lateral pressure. In solids, however, shear forces help in propagating the disturbance in the lateral direction as well. Hence,...
Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

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. We can...

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Related Experiment Video

Updated: May 18, 2026

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

Surface waves on a half space with depth-dependent properties.

Oluwaseyi Balogun1, Jan D Achenbach

  • 1Northwestern University, McCormick School of Engineering and Applied Science, Center for Quality Engineering and Failure Prevention, 2137 N. Tech Drive, Catalysis Building, Room 327, Evanston, Illinois 60208-3020, USA. o-balogun@northwestern.edu

The Journal of the Acoustical Society of America
|September 18, 2012
PubMed
Summary
This summary is machine-generated.

This study analyzes high-frequency surface wave dispersion in depth-varying elastic materials. Simple expressions for wave velocity and displacement were derived, showing excellent agreement with numerical models for layered approximations.

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Last Updated: May 18, 2026

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Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations
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Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Published on: August 21, 2018

Area of Science:

  • Solid Mechanics
  • Geophysics
  • Wave Propagation

Background:

  • Surface waves are crucial for understanding seismic activity and material properties.
  • Analyzing wave dispersion in heterogeneous media is complex.
  • Depth-dependent elastic properties significantly influence wave behavior.

Purpose of the Study:

  • To analyze the dispersive properties of surface waves in an isotropic elastic body with depth-varying elastic moduli and mass density.
  • To derive simplified analytical expressions for displacements and stresses in the high-frequency range.
  • To investigate the relationship between surface wave velocity and wavenumber for specific material property variations.

Main Methods:

  • High-frequency approximation for surface wave analysis.
  • Derivation of dispersion equation from vanishing surface traction conditions.
  • Comparison of analytical results with numerical simulations of layered media.

Main Results:

  • Obtained simple expressions for displacements and stresses.
  • Derived a dispersion equation relating surface wave velocity to wavenumber.
  • Demonstrated exponential decay of displacement amplitudes with depth.
  • Achieved excellent agreement between analytical and numerical results for various material property profiles.

Conclusions:

  • The high-frequency approximation provides accurate analytical solutions for surface wave dispersion in depth-varying elastic media.
  • The derived dispersion equation is valid for specific material property dependencies.
  • Numerical models based on layering effectively approximate continuous inhomogeneity for surface wave analysis.