# Dictionary:Q

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):

${\displaystyle {\frac {1}{Q}}={\frac {\alpha V}{\pi f}}={\frac {\alpha \lambda }{\pi }}={\frac {hT}{\pi }}={\frac {\delta }{\pi }}={\frac {2\Delta f}{f_{\mathrm {r} }}}}$

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

${\displaystyle A\mathrm {e} ^{-\alpha x}\sin 2\pi f(t-{\tfrac {x}{V}})}$

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 ${\displaystyle \Delta f}$ is the change in frequency that reduces the amplitude by ${\displaystyle {\frac {1}{\sqrt {2}}}}$. The damping factor h relates to the decrease in amplitude with time,

${\displaystyle A(t)=A_{0}\mathrm {e} ^{-ht}\cos \omega t\ }$

Absorption terminology. Sometimes this terminology is used for attenuation because of factors other than absorption. E = energy, ${\displaystyle \Delta E}$ = energy lost in one cycle, ${\displaystyle \lambda }$ = wavelength, f = frequency, x = distance, t = time, ${\displaystyle {\frac {A}{A_{0}}}={\frac {\text{amplitude}}{\text{initial amplitude}}}}$, ${\displaystyle {\frac {A_{1}}{A_{2}}}={\frac {\text{amplitude}}{\text{amplitude one cycle later}}}}$.[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.