Editing Quasinormal mode (section)

==Example==
A familiar example is the perturbation (gentle tap) of a wine glass with a knife: the glass begins to ring, it rings with a set, or superposition, of its natural frequencies — its modes of sonic energy dissipation. One could call these modes ''[[Normal mode|normal]]'' if the glass went on ringing forever. Here the amplitude of oscillation decays in time, so we call its modes ''quasi-normal''. To a high degree of accuracy, '''quasinormal''' ringing can be approximated by

:<math>\psi(t) \approx e^{-\omega^{\prime\prime}t}\cos\omega^{\prime}t</math>

where <math>\psi\left(t\right)</math> is the amplitude of oscillation,
<math>\omega^{\prime}</math> is the frequency, and
<math>\omega^{\prime\prime}</math> is the decay rate.  The quasinormal
frequency is described by two numbers,

:<math>\omega = \left(\omega^{\prime} , \omega^{\prime\prime}\right)</math>

or, more compactly

:<math>\psi\left(t\right) \approx \operatorname{Re}(e^{i\omega t})</math>

:<math>\omega =\omega^{\prime} + i\omega^{\prime\prime}</math>

Here, <math>\mathbf{\omega}</math> is what is commonly referred to as the
'''quasinormal mode frequency'''. It is a [[complex number]] with two pieces of information: real part is the temporal oscillation; imaginary part is the temporal, [[exponential decay]].

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In certain cases the amplitude of the wave decays quickly, to follow the decay for a longer time one may plot <math>\log\left|\psi(t)\right|</math>

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{{listen |filename=qnm.ogg |title=The sound of quasinormal ringing |description=}}