Difference between revisions of "Dictionary:Q(Quality)"

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<center><math>A\mathrm{e}^{-\alpha x} \sin 2 \pi f ( t - \tfrac{x}{V} ) </math></center>
 
<center><math>A\mathrm{e}^{-\alpha x} \sin 2 \pi f ( t - \tfrac{x}{V} ) </math></center>
  
where ''x'' is the distance traveled. The [[Dictionary:logarithmic decrement|logarithmic decrement]] ''&delta;'' is the natural log of the ratio of the amplitudes of two successive cycles. The last equation above relates ''Q'' to the sharpness of a resonance condition; ''f''<sub>r</sub> is the resonance frequency and &Delta;''f'' is the change in frequency that reduces the amplitude by 1/&#x221A;2. The [[Dictionary:damping factor|damping factor]] ''h'' relates to the decrease in amplitude with time,  
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where ''x'' is the distance traveled. The [[Dictionary:logarithmic decrement|logarithmic decrement]] ''&delta;'' is the natural log of the ratio of the amplitudes of two successive cycles. The last equation above relates ''Q'' to the sharpness of a resonance condition; <math>f_{r}</math> is the resonance frequency and <math>\Delta f</math> is the change in frequency that reduces the amplitude by <math>\frac{1}{\sqrt{2}}</math>. The [[Dictionary:damping factor|damping factor]] ''h'' relates to the decrease in amplitude with time,  
  
 
<center><math>A(t) = A_0\mathrm{e}^{-ht} \cos \omega t \ </math></center>
 
<center><math>A(t) = A_0\mathrm{e}^{-ht} \cos \omega t \ </math></center>

Revision as of 12:23, 30 December 2014

1. Quality factor, the ratio of 2π times the peak energy to the energy dissipated in a cycle; the ratio of 2π times the power stored to the power dissipated. The seismic Q of rocks is of the order of 50 to 300. Q is related to other measures of absorption (see below):

where V, f, λ, and T are, respectively, velocity, frequency, wavelength, and period.[1] The absorption coefficient α is the term for the exponential decrease of amplitude with distance because of absorption; the amplitude of plane harmonic waves is often written as

where x is the distance traveled. The logarithmic decrement δ is the natural log of the ratio of the amplitudes of two successive cycles. The last equation above relates Q to the sharpness of a resonance condition; is the resonance frequency and is the change in frequency that reduces the amplitude by . The damping factor h relates to the decrease in amplitude with time,

See Figure A-2.

2. The ratio of the reactance of a circuit to the resistance.

3. A term to describe the sharpness of a filter; the ratio of the midpoint frequency to the bandpass width (often at 3 dB).

4. A designation for Love waves (q.v.).

5. Symbol for the Koenigsberger ratio (q.v.).

6. See Q-type section.

See also

References

  1. Sheriff, R. E. and Geldart, L. P., 1995, Exploration Seismology, 2nd Ed., Cambridge Univ. Press.