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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 pressures...

Sound Waves

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,...

Reflection of Waves

Reflection of Waves

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...

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.

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...

Modes of Standing Waves - I

Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This phenomenon...

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Related Experiment Video

Updated: Jun 3, 2026

Blast Quantification Using Hopkinson Pressure Bars

Blast Quantification Using Hopkinson Pressure Bars

Published on: July 5, 2016

Burnett-Cattaneo continuum theory for shock waves.

Brad Lee Holian¹, Michel Mareschal, Ramon Ravelo

¹Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

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

|March 17, 2011

Summary

This study models shock wave propagation using a refined continuum theory. The new model accurately predicts fluid behavior under strong shock conditions, aligning with molecular dynamics simulations.

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Area of Science:

Physics
Fluid Dynamics
Thermodynamics

Background:

Shock waves are fundamental phenomena in fluid dynamics.
Understanding shock wave propagation in dense fluids is crucial for various applications.
Previous models often simplified the complex kinetic processes within shock fronts.

Purpose of the Study:

To develop a refined continuum theory for modeling strong shock wave propagation.
To incorporate nonlinear effects and kinetic temperature relaxation into shock wave models.
To achieve quantitative agreement with molecular dynamics simulations.

Main Methods:

Modeling shock wave propagation in ideal gas and Lennard-Jones fluids.
Accounting for cold compression via nonlinear strain-rate dependent thermal conductivity.
Applying the Cattaneo-Maxwell relaxation equation to kinetic temperature components.

Main Results:

The refined theory accurately models shock wave propagation, including cold compression effects.
Kinetic temperature relaxation is quantitatively addressed near the shock front.
The model shows nearly quantitative agreement with nonequilibrium molecular-dynamics simulations.

Conclusions:

The new continuum theory provides a more accurate description of strong shock waves.
The incorporation of nonlinear Burnett terms and temperature relaxation is key to the model's success.
This work advances the understanding of non-equilibrium phenomena in shock-compressed fluids.