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Rarefaction is the reduction of a medium's density, or the opposite of compression.
A natural example of this is as a phase in a sound wave or phonon. Half of a sound wave is made up of the compression of the medium, and the other half is the decompression or rarefaction of the medium.
Another natural example of rarefaction is in the layers of our atmosphere. Because what constitutes our atmosphere has mass, it is definite that most of the atmospheric matter will be nearer to the Earth. Therefore, air at higher layers of the atmosphere is considered to have less pressure, or is rarefied in relation to air at lower layers.
Rarefaction can be easily observed by compressing a spring and releasing it.
Rarefaction waves expand with time; for most gases the rarefaction wave keeps the same overall profile at all times (it is a 'self-similar expansion'). Each part of the wave travels at the local speed of sound, in the local medium. This expansion behaviour is in contrast to the behaviour of pressure increases, which get narrower with time, until they steepen into shock waves.
Rarefaction can refer to an area of low relative pressure following a shockwave.
The term rarefaction in ecology refers to a technique to standardize and compare species richness computed from samples of different sizes. Rarefaction allows the calculation of the species richness for a given number of sampled individuals and allows the construction of so called rarefaction curves. This curve is a plot of the number of species as a function of the number of individuals sampled. In case of a steep slope a large fraction of the species diversity is not sampled, if the part of the curve is already becoming flat, a reasonable number of individuals is sampled and more intensive sampling will probably only yield a small number of additional species (if any). 
Rarefaction only occurs in a longitudinal wave. The wave consists of zones of compression (where the waves are squeezed together) and rarefaction (where the waves are stretched out.) Think of a big spring, like a Slinky, held horizontal. Pinch a bunch of coils together with your thumb and finger. That is compression. The coils to either side, where they are stretched out toward where you are pinching the others together, are rarefied. This is how sound waves act when they travel.
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Rarefaction occurs only in a______wave.?
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A longitudinal wave has consecutive compressions and rarefactions. A good example of longitudinal wave is "sound wave"
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Because the direction in which the disturbance is caused is the same as the direction in which the wave is travelling. therefore, it is called a longitudinal wave as opposed to a transverse wave in which the direction in which the disturbance is caused is perpendicular to the direction in which the wave travels. i hope this answers your question.