harmonic hamâhang (#) Fr.: harmonique (adj.) Of, pertaining to, or noting a series of oscillations in
which each oscillation has a frequency that is an integral multiple of the same basic
frequency. From L. harmonicus, from Gk. harmonikos "harmonic, musical," from harmonia "agreement, concord of sounds," related to harmos "joint," arariskein "to join together;" PIE base *ar- "to fit together." Hamâhang, "harmonious, concordant," from ham- "together, with; same, equally, even" (Mid.Pers. ham-, like L. com- and Gk. syn- with neither of which it is cognate. O.Pers./Av. ham-; Skt. sam-; also O.Pers./Av. hama- "one and the same," Skt. sama-; Gk. homos-; originally identical with PIE numeral *sam- "one," from *som-) + âhang "melody, pitch, tune; harmony, concord," from Proto-Iranian *āhang-, from prefix ā- + *hang-, from PIE base *seng^{w}h- "to sing, make an incantation;" cf. O.H.G. singan; Ger. singen; Goth. siggwan; Swed. sjunga; O.E. singan "to chant, sing, tell in song;" maybe cognate with Gk. omphe "voice; oracle." |
harmonic mean miyângin-e hamâhang Fr.: moyenne harmonique A number whose reciprocal is the → arithmetic mean of the reciprocals of a set of numbers. Denoted by H, it may be written in the discrete case for n quantities x_{1}, ..., x_{n}, as: 1/H = (1/n) Σ(1/x_{i}), summing from i = 1 to n. For example, the harmonic mean between 3 and 4 is 24/7 (reciprocal of 3: 1/3, reciprocal of 4: 1/4, arithmetic mean between them 7/24). The harmonic mean applies more accurately to certain situations involving rates. For example, if a car travels a certain distance at a speed speed 60 km/h and then the same distance again at a speed 40 km/h, then its average speed is the harmonic mean of 48 km/h, and its total travel time is the same as if it had traveled the whole distance at that average speed. However, if the car travels for a certain amount of time at a speed v and then the same amount of time at a speed u, then its average speed is the arithmetic mean of v and u, which in the above example is 50 km/h. |
harmonic motion jonbeš-e hamâhang (#) Fr.: mouvement harmonique A motion that repeats itself in equal intervals of time (also called periodic motion). |
harmonic oscillator navešgar-e hamâhang (#) Fr.: oscillateur harmonique Any oscillating particle in harmonic motion. → harmonic; → oscillator. |
harmonic progression farâyâzi-ye hamâhang Fr.: progression harmonique Math.: Any ordered set of numbers, the reciprocals of which have a constant difference between them. For example 1, ½, 1/3, ¼, ..., 1/n. Also called → harmonic sequence. → harmonic; progression. |
harmonic sequence peyâye-ye hamâhang Fr.: suite harmonique |
harmonic series seri-ye hamâhang Fr.: série harmonique Overtones whose frequencies are integral multiples of the → fundamental frequency. The fundamental frequency is the first harmonic. |
simple harmonic motion jonbeš-e hamâhang-e sâdé Fr.: mouvement harmonique The motion of a body subjected to a restraining force which is directly proportional to the displacement from a fixed point in the line of motion. The equation of simple harmonic motion is given by x = A sin(ωt + θ_{0}), where x is the body's displacement from equilibrium position, A is the → amplitude, or the magnitude of harmonic oscillations, ω is the → angular frequency, t is the time elapsed, and θ_{0} is the → initial phase angle. |
simple harmonic oscillator navešgar-e hamâhang-e sâdé Fr.: oscillateur harmonique simple An oscillator whose force is proportional to its extension, according to → Hooke's law. The way the oscillator moves is called → simple harmonic motion. → simple; → harmonic; → oscillator. |
spherical harmonic hamâhang-e kore-yi Fr.: fonction harmonique sphérique A solution of some mathematical equations when → spherical polar coordinates are used in investigating physical problems in three dimensions. For example, solutions of → Laplace's equation treated in spherical polar coordinates. Spherical harmonics are ubiquitous in atomic and molecular physics and appear in quantum mechanics as → eigenfunctions of → orbital angular momentum. They are also important in the representation of the gravitational and magnetic fields of planetary bodies, the characterization of the → cosmic microwave background anisotropy, the description of electrical potentials due to charge distributions, and in certain types of fluid motion. The term spherical harmonics was first used by William Thomson (Lord Kelvin) and Peter Guthrie Tait in their 1867 Treatise on Natural Philosophy; → spherical; → harmonic. |