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

Line 8: | Line 8: | ||

<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]] ''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; < | + | where ''x'' is the distance traveled. The [[Dictionary:logarithmic decrement|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; ''f''<sub>r</sub> is the resonance frequency and Δ''f'' is the change in frequency that reduces the amplitude by 1/√2. 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 13:32, 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; *f*_{r} is the resonance frequency and Δ*f* is the change in frequency that reduces the amplitude by 1/√2. 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

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