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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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Updated: Jun 24, 2026

Subsurface Defect Localization by Structured Heating Using Laser Projected Photothermal Thermography

Subsurface Defect Localization by Structured Heating Using Laser Projected Photothermal Thermography

Published on: May 15, 2017

Laser induced thermal-wave fields in bilayered spherical solids.

Guangxi Xie¹, Zhifeng Chen, Chinhua Wang

¹Key Laboratory of Modern Optical Technologies of Jiangsu Province, Institute of Modern Optical Technologies, Soochow University, Suzhou, Jiangsu 215006, People's Republic of China.

The Review of Scientific Instruments

|April 2, 2009

Summary

A new theoretical model evaluates heat diffusion in bilayered spheres using thermal waves. This method accurately determines material thermal diffusivity from experimental data.

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Last Updated: Jun 24, 2026

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Published on: February 4, 2017

Area of Science:

Physics
Materials Science
Heat Transfer

Background:

Understanding heat transfer in layered spherical materials is crucial for various applications.
Previous models often lack the flexibility to handle arbitrary laser beam profiles.

Purpose of the Study:

To develop a theoretical model for analyzing thermal wave propagation in bilayered spherical samples.
To provide a method for deducing thermal properties of materials from photothermal measurements.

Main Methods:

Utilizing the Green's function method to derive the thermal-wave Green's function for bilayered spherical structures.
Analyzing the thermal-wave field characteristics based on material properties, sample dimensions, and laser beam parameters.
Employing laser infrared photothermal radiometry for experimental validation.

Main Results:

The derived Green's function accurately describes thermal wave fields for arbitrary laser intensity distributions.
The model's predictions show sensitivity to thermal diffusivity, sample diameter, beam size, and measurement angle.
Experimental data from steel spheres were successfully fitted to the theoretical model.

Conclusions:

The Green's function method offers a robust framework for evaluating thermal properties of bilayered spheres.
The study successfully deduced the thermal diffusivities of steel spheres.
The theoretical model provides a valuable tool for non-destructive material characterization.