Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Equations of Wave Motion

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.

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:

Sound as Pressure Waves

Sound as Pressure Waves

Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
The pressure fluctuation depends on the difference in displacements between the successive points in the...

Graphing the Wave Function

Graphing the Wave Function

Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.

Velocity and Acceleration of a Wave

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...

The de Broglie Wavelength

The de Broglie Wavelength

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...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Hypertension Control in Low-Income Patients.

The New England journal of medicine·2026

Same author

Cell-based screen identifies translation state modulators that extend lifespan in D. melanogaster and C. elegans.

The journals of gerontology. Series A, Biological sciences and medical sciences·2026

Same author

Hydroxyl Radical-Driven Methanogenesis in Sunlit Surface Waters.

Environmental science & technology·2026

Same author

Development and validation of a predictive model for short-term symptom relief after organophosphate poisoning.

Frontiers in medicine·2026

Same author

Platelet-rich plasma therapy for low back pain: A comprehensive systematic review and meta-analysis.

Journal of back and musculoskeletal rehabilitation·2026

Same author

Bidirectional regulation between circadian feeding behavior and specialized midgut clocks in <i>Drosophila</i>.

bioRxiv : the preprint server for biology·2026

Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

See all related articles

Search research articles

Related Experiment Video

Updated: May 18, 2026

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces

Published on: July 26, 2016

Mathieu function solutions for photoacoustic waves in sinusoidal one-dimensional structures.

Binbin Wu¹, Gerald J Diebold

¹Brown University, Department of Chemistry, Providence, RI 02912, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

This summary is machine-generated.

Researchers explored the photoacoustic effect in structures with spatially varying sound speeds. New mathematical solutions reveal how optical radiation generates acoustic waves and their behavior in phononic structures.

More Related Videos

Three-dimensional Optical-resolution Photoacoustic Microscopy

Three-dimensional Optical-resolution Photoacoustic Microscopy

Published on: May 3, 2011

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Related Experiment Videos

Last Updated: May 18, 2026

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces

Published on: July 26, 2016

Three-dimensional Optical-resolution Photoacoustic Microscopy

Three-dimensional Optical-resolution Photoacoustic Microscopy

Published on: May 3, 2011

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Area of Science:

Acoustics
Optics
Materials Science

Background:

The photoacoustic effect links light absorption to sound generation.
Understanding acoustic wave propagation in structured materials is crucial for device design.

Purpose of the Study:

To investigate the photoacoustic effect in a 1D structure with spatially modulated sound speed.
To develop new mathematical tools for analyzing acoustic wave behavior in phononic structures.

Main Methods:

Governing equation: inhomogeneous Mathieu equation derived from photoacoustic effect.
Mathematical solutions: orthogonality relations, traveling wave Mathieu functions, Floquet solutions.
Analysis of acoustic wave characteristics: band gaps, damping, dispersion, and confinement.

Main Results:

Identified governing inhomogeneous Mathieu equation for the photoacoustic effect.
Developed novel mathematical solutions and wave characteristics for phononic structures.
Demonstrated acoustic confinement and subharmonic generation within band gaps.

Conclusions:

The study provides a comprehensive theoretical framework for photoacoustic wave phenomena in phononic crystals.
New mathematical solutions offer insights into acoustic wave control and manipulation.
Findings are relevant for designing advanced acoustic and optical devices.