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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:

Shock Waves

Shock Waves

While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high...

Sound Waves: Interference

Sound Waves: Interference

Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure waves. When two identical waves from the same source superimpose on each other, the combination of two crests or two troughs results in amplitude reinforcement known as constructive interference. If two identical waves, that are initially in phase, become out of phase because of different path lengths, the combination of crests with troughs...

Modes of Standing Waves: II

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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....

Sound Waves: Resonance

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Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...

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When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...

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Related Experiment Video

Updated: Sep 30, 2025

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

Published on: August 27, 2013

Extended topological valley-locked surface acoustic waves.

Ji-Qian Wang^1,2, Zi-Dong Zhang¹, Si-Yuan Yu^3,4,5

¹National Laboratory of Solid State Microstructures & College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, China.

Nature Communications

|March 15, 2022

Summary

Researchers demonstrated robust, tunable surface acoustic wave (SAW) transport using topological phononic crystals. This breakthrough enables flexible on-chip acoustic manipulation for advanced information processing and sensing applications.

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Area of Science:

Condensed matter physics
Acoustics
Materials science

Background:

Topological valley-contrasting materials offer robust wave transport.
Surface acoustic waves (SAWs) are crucial for classical wave guiding.

Purpose of the Study:

To experimentally realize and investigate valley-locked edge transport for SAWs.
To extend 1D edge transport to quasi-2D by doping.
To demonstrate robustness and tunability for acoustic manipulation.

Main Methods:

Design and fabrication of miniaturized phononic crystals on a substrate.
Experimental realization of valley-locked edge transport for SAWs.
Doping phononic crystal boundaries to create SAW Dirac "semimetal" layers.

Main Results:

Achieved valley-locked edge transport for SAWs.
Extended 1D edge transport to quasi-2D.
Demonstrated robustness against bending and defects.
Showcased configurable on-chip acoustic manipulation (routing, focusing, splitting, converging).

Conclusions:

Topological phononic crystals enable robust and flexible SAW manipulation.
This approach facilitates the development of hybrid phononic circuits for acoustic information processing and sensing.