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Propagation of Waves

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 Waves in a Cavity

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:

Travelling Waves

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;...

Modes of Standing Waves: II

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.

Plane Electromagnetic Waves I

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...

Standing Waves

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...

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Related Experiment Video

Updated: Jul 15, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Wave propagation along transversely periodic structures.

Mihai V Predoi¹, Michel Castaings, Bernard Hosten

¹Department of Mechanics, University Politehnica Bucharest, Splaiul Independentei, Bucharest, Romania. predoi@cat.mec.pub.ro

The Journal of the Acoustical Society of America

|May 3, 2007

Summary

This study enhances the semianalytical finite element method for analyzing guided waves in periodic structures. The improved method reveals new insights into wave propagation and mode characteristics, crucial for ultrasonic non-destructive evaluation (NDE).

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Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

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Published on: November 30, 2012

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Last Updated: Jul 15, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

Published on: November 30, 2012

Area of Science:

Solid mechanics
Wave propagation physics
Materials science

Background:

Dispersion curves for guided waves are fundamental for non-destructive evaluation (NDE) ultrasonic applications.
Studying wave propagation in periodic structures requires advanced computational methods.

Purpose of the Study:

To present an evolution of the semianalytical finite element method (SAFEM).
To illustrate improvements in SAFEM for analyzing guided wave propagation in infinite periodic structures.
To investigate dispersion curves and field characteristics for guided modes in complex structures.

Main Methods:

Application of the semianalytical finite element method (SAFEM).
Utilizing periodic boundary conditions to model infinite periodicity.
Theoretical and experimental investigation of wave propagation.

Main Results:

The enhanced SAFEM allows a complete investigation of dispersion curves and displacement/stress fields.
Specific and original guided modes were identified in a grooved aluminum plate.
The method is applicable to anisotropic and absorbing periodic structures.

Conclusions:

The improved SAFEM offers significant advancements for studying guided wave propagation.
The findings are vital for developing sophisticated NDE ultrasonic techniques.
The method successfully identifies unique guided modes in periodic structures.