Dictionary:Q

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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):

1/QVf=αλ/π=hT/π=δ/π=2Δf/fr,


where V, f, λ, and T are, respectively, velocity, frequency, wavelength, and period (see Sheriff and Geldart, 1995: 60, 177). 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

Ae–αxsin2πf(tx/V),


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; fr is the resonance frequency and Δf is the change in frequency that reduces the amplitude by 1/√2. The damping factor h relates to the decrease in amplitude with time,

A(t)=Aoehtcosωt.


See also 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.