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Time Dependent Wave Equation 1D One Dimensional Optical Resonator Modes
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Inelastic Collision Conversion to Internal Energy Brownian Motion Animation 2D Using Hard Sphere Scattering Large Disc Kinetics 2D Condensation of a Gas on a 2D Solid Maxwell's Demon Energy Seperator 2D Minimize Final Energy 2D and 3D Gas Diffusion 2D Gas Expansion 2D Linear Gas Expansion 2D Constant Pressure Gas Expansion 2D Circular Gas Explosion 2D Circular MagnetoCaloric Effect 2D Convection Loops in a Numerical Gas Chapter 3: Gas Energy Equipartition Energy Equipartition of a Two Dimensional Gas with Two Different Masses Energy Equipartition of a Three Dimensional Gas with Two Different Masses Gas Energy Equipartition 3D
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Tumbling Block on Inclined Plane New Roller on Inclined Plane Sliding Block on Inclined Plane Classic Objects Motion 1D Generation of Curve for Fastest Time between Two Points Curve for Fastest Time between Two Points Bead Sliding On a Stiff Wire Sound Wave in Two Solid Media Mechanical Properties of a 2D Numerically Modeled Lattice Vibrating Reed Numerical Model 2D Laminar Flow of a Fluid in a 2D Bearing Animation of a Fountain 2D Gravity Leveling of a 2D Liquid Longitudinal and Shear Wave Sound Speed in a 2D Lattice Mechanical Properties of a 2D Numerically Modeled Lattice Vibration Frequencies of a 2D Numerically Modeled Lattice Damped Harmonic Oscillator Motion and Modes of a Particle in a Mexican Hat Potential Forced Oscillator Roller Bearing Cam and Roller Follower Simple Hybrid Gear Train Ratchet Animation Child's Swing Height Increase Mechanics Roller Chain Animation Elasticity of 3D Gas Driving a Piston Free to Forced Harmonic Oscillator Transition Physics of Mounting a Tire on a Rim Physics of a Pendulum Clock Escapement Physics of a Gas Pressure Gauge
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Physics of a Gas Pressure Gauge Ion Drift in Neutral Particle Sea Diffusion Equation Solved by Finite Difference Method Linear Particle Diffusion Heat Flow 1D with Time Dependent Boundary Solid Cube in Liquid Column Drag on a Large Sphere Due to a Digital Gas Animation of a Gas Centrifuge Laminar Flow of a Gas in an Annular Space Laminar Flow of a Fluid in a 2D Bearing Incompressible Fluid Flow through a Constriction Fluid Flow Due To Pressure Gradients
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Semiconductor Electron Energies and Band Gap 1D Semiconductor Electron Energies and Band Gap 2D Simple Fermi Surface p-nJunctionDiode Depletion Width Temperature Dependence of 2D Fermi-Dirac Particles
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Assembly of 3D Parts Using Javascript Web Graphics Library 3D Compared to Javascript 3D Graphics 3D Graphics Tutorial Beginnings Proof of Pythagoras a^2+b^2=c^2
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Multiple Slider Animation Template for Plotting with HTML Enhanced Sliders or Ranges Collapsible Dropdown Menu Example Arrow Functions Fast Fourier Transform (FFT) Demonstration
Animation of a Progress Bar
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Time Dependent Wave Equation 1D One Dimensional Optical Resonator Modes
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
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Chapter 11
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Probability of Birthday Match Random Creation of Probability Function Profiles Two Dies Probability Distribution Three Dies Probability Distribution
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Light Rays in a Transparent Isosceles Prism Light Ray in a Series of Wedges of Various Index of Refraction Snells Law of Refraction Refraction Due to Dipoles in Two Media Refraction and Reflection Two Media Animation of Concave Mirror Reflection Animation of Convex Lens Refraction Prism Refraction-Wave Picture Thick Lens Ray Trace Monochromator (Czerny-Turner Type) Wavelets from Concave Mirror> Thick Lens Focusing
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Sagnac Effect Fiber Optical Gyro (FOG) Ring Laser Gyro (RLG)
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Paticle Motion in a Venturi: Wall Reflections Paticle Motion in a Venturi Potential Elliptical Ion Trap Using Boundary Potential Distribution Prediction of Hard Disc Collision Time and Position Rigid Rotor Collisions
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Acoustic Wave with Built-in Pressure Acoustic Waves in 2D Numerically Modeled Solid Wave 1D on a Linear Array Waves on Discrete Model of Vibrating String Linear Acoustic Wave in a 3D Gas Spherical Acoustic Wave in a 3D Gas Laterally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces Longitudinally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces
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Scattering from a Crystalline Target 2D Scattering from a Crystalline Target 3D
Chapter 4
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Chapter 6
Chapter 7
Chapter 8
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Chapter 12
Energy Conduction in a 2D Numerically Modeled Solid Lattice Unbalanced Gas Dynamics:Energy Flow in a Gas
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
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Chapter 12

Hover over the menu bar to pick a physics animation.

Linear Acoustic Wave in 3D Atomic Gas

This animation considers the possibility of visualizing a sound wave in a hard sphere mono-atomic gas. It is well known that sound waves in gases are longitudinal temporal and spatial pressure variations and these are usually sinusoidal of the form:

`P(x,t)=P_0+deltaPcos(omegat-kx+phi_P)`

where `P_0` is the ambient pressure, the amplitude `deltaP` is a very small fraction of `P_0`, `omega` is the radian temporal frequency and `k` is the radian spatial frequency while `t` is time and `x` is spatial extent and `phi_P` is just a constant which adjusts the phase at x=0 and t=0. If there is no dispersion then an expression for `k` is `k=omega/c` where c is the speed of the sound wave.

One of the goals of this animation is to determine the quantity `lambda=(2pi)/k=2pic/omega` which, for a given `omega`, effectively determines c.

The pressure fluctuations amplitudes are very small fractions of the average pressure so it is necessary to subtract off the mean pressure in order to see the very small pressure fluctuations. Even after this subtraction is done, we still have to consider the statistical variation, due to very limited numbers of atoms that can be handled by the computer, of the average pressure per longitudinal bin of the gas. For that reason, we have to resort to Fast Fourier Transform (FFT) in order to discern the true spatial frequency of the pressure variation. With the FFT we have the advantage that we can average the observed frequency content over very many piston cycles and thereby see the true pressure or density variation spectrum that is induced.

Description of the Plots:

Top: Shows moving atoms (red) and moving piston (gray) for ideal sound wave.
Next Lower: Shows direct plot of the energy and density bin data as a function of position x as well as Fast Fourier transforms (FFTs) of energy (green) and density (red).
Next Lower: Shows moving atoms (red) and moving piston (gray) for the sound wave induced by the piston.
Bottom: A moving plot (red) of the density obtained by the time scan at the bin position given by the "x position of time scan" slider as well as the accumulated FFT (green) of this time scan. The expected frequency of this time scan is marked by the green vertical line.
It should be noted that the peak of the expected frequency of the FFT of this scan washes out badly if the scan distance from the piston is any larger than about 100. This effect would have been expected for a spherical wave where the amplitude is expected to follow a 1/r^2 curve but not for this linear geometry. The cause must be the inter-particle scattering, which is essentially diffusion of the density maxima.

The following parameters are learner adjustable:
1. Starting Energy of Each Atom (actually a disc since this is a 2D animation)
2. Total Number of Atoms
3. Piston angular Frequency (radians per second)
4. Piston Motion Amplitude
5. Number of Bins for the Energy or Density Distributions
6. Total Length of Cylinder
7. Number of Animation Frames for Bin Storage (without accumulation, bin data would be very noisy)
8. x Position of the Density Time Scan
9. Width of the Time Scan Bin

Summary and Conclusions

Comparing the FFT plot of the Actual Gas Density "Wave" to the Ideal Gas Density Wave we see that the actual gas density has no significant wave-like behavior.
Conclusion is that sound waves in a gas cannot be simulated by simple hard sphere scattering interaction.