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Rarefaction is the reduction of an item's density, the opposite of compression. [1] Like compression, which can travel in waves ( sound waves , for instance), rarefaction waves also exist in nature. A common rarefaction wave is the area of low relative pressure following a shock wave (see picture).
The Riemann problem is very useful for the understanding of equations like Euler conservation equations because all properties, such as shocks and rarefaction waves, appear as characteristics in the solution. It also gives an exact solution to some complex nonlinear equations, such as the Euler equations.
Namely the rarefaction wave, the contact discontinuity and the shock discontinuity. If this is solved numerically, one can test against the analytical solution, and get information how well a code captures and resolves shocks and contact discontinuities and reproduce the correct density profile of the rarefaction wave.
It restores the missing rarefaction wave by using an estimation technique, such as linearisation. More advanced techniques exist, like using the Roe average velocity for the middle wave speed. These schemes are quite robust and efficient but somewhat more diffusive. [9]
"Longitudinal waves" and "transverse waves" have been abbreviated by some authors as "L-waves" and "T-waves", respectively, for their own convenience. [1] While these two abbreviations have specific meanings in seismology (L-wave for Love wave [2] or long wave [3]) and electrocardiography (see T wave), some authors chose to use "ℓ-waves" (lowercase 'L') and "t-waves" instead, although they ...
The rarefaction is the farthest distance apart in the longitudinal wave and the compression is the closest distance together. The speed of the longitudinal wave is increased in higher index of refraction, due to the closer proximity of the atoms in the medium that is being compressed. Sound is a longitudinal wave.
Sound is a pressure wave, which consists of alternating periods of compression and rarefaction.A noise-cancellation speaker emits a sound wave with the same amplitude but with an inverted phase (also known as antiphase) relative to the original sound.
Zero sound is the name given by Lev Landau in 1957 to the unique quantum vibrations in quantum Fermi liquids. [1] The zero sound can no longer be thought of as a simple wave of compression and rarefaction, but rather a fluctuation in space and time of the quasiparticles' momentum distribution function.