To relinquish; to give up claim to; not to insist on or claim; to refuse; to forego. [1913 Webster] He waiveth milk, and flesh, and all. --Chaucer. [1913 Webster] We absolutely do renounce or waive our own opinions, absolutely yielding to the direction of others. --Barrow. [1913 Webster]
To throw away; to cast off; to reject; to desert. [1913 Webster]
(Law) (a) To throw away; to relinquish voluntarily, as a right which one may enforce if he chooses. (b) (O. Eng. Law) To desert; to abandon. --Burrill. [1913 Webster] Note: The term was applied to a woman, in the same sense as outlaw to a man. A woman could not be outlawed, in the proper sense of the word, because, according to Bracton, she was never in law, that is, in a frankpledge or decennary; but she might be waived, and held as abandoned. --Burrill. [1913 Webster]
Wave \Wave\ (w[=a]v), v. t. See Waive. --Sir H. Wotton. --Burke. [1913 Webster]
Wave \Wave\, v. i. [imp. & p. p. Waved; p. pr. & vb. n. Waving.] [OE. waven, AS. wafian to waver, to hesitate, to wonder; akin to w[ae]fre wavering, restless, MHG. wabern to be in motion, Icel. vafra to hover about; cf. Icel. v[=a]fa to vibrate. Cf. Waft, Waver.] [1913 Webster]
To play loosely; to move like a wave, one way and the other; to float; to flutter; to undulate. [1913 Webster] His purple robes waved careless to the winds. --Trumbull. [1913 Webster] Where the flags of three nations has successively waved. --Hawthorne. [1913 Webster]
To be moved to and fro as a signal. --B. Jonson. [1913 Webster]
To fluctuate; to waver; to be in an unsettled state; to vacillate. [Obs.] [1913 Webster] He waved indifferently 'twixt doing them neither good nor harm. --Shak. [1913 Webster]
Wave \Wave\, v. t.
To move one way and the other; to brandish. "[Aeneas] waved his fatal sword." --Dryden. [1913 Webster]
To raise into inequalities of surface; to give an undulating form a surface to. [1913 Webster] Horns whelked and waved like the enridged sea. --Shak. [1913 Webster]
To move like a wave, or by floating; to waft. [Obs.] --Sir T. Browne. [1913 Webster]
To call attention to, or give a direction or command to, by a waving motion, as of the hand; to signify by waving; to beckon; to signal; to indicate. [1913 Webster] Look, with what courteous action It waves you to a more removed ground. --Shak. [1913 Webster] She spoke, and bowing waved Dismissal. --Tennyson. [1913 Webster]
Wave \Wave\, n. [From Wave, v.; not the same word as OE. wawe, waghe, a wave, which is akin to E. wag to move. [root]138. See Wave, v. i.] [1913 Webster]
An advancing ridge or swell on the surface of a liquid, as of the sea, resulting from the oscillatory motion of the particles composing it when disturbed by any force their position of rest; an undulation. [1913 Webster] The wave behind impels the wave before. --Pope. [1913 Webster]
(Physics) A vibration propagated from particle to particle through a body or elastic medium, as in the transmission of sound; an assemblage of vibrating molecules in all phases of a vibration, with no phase repeated; a wave of vibration; an undulation. See Undulation. [1913 Webster]
Water; a body of water. [Poetic] "Deep drank Lord Marmion of the wave." --Sir W. Scott. [1913 Webster] Build a ship to save thee from the flood, I 'll furnish thee with fresh wave, bread, and wine. --Chapman. [1913 Webster]
Unevenness; inequality of surface. --Sir I. Newton. [1913 Webster]
A waving or undulating motion; a signal made with the hand, a flag, etc. [1913 Webster]
The undulating line or streak of luster on cloth watered, or calendered, or on damask steel. [1913 Webster]
Something resembling or likened to a water wave, as in rising unusually high, in being of unusual extent, or in progressive motion; a swelling or excitement, as of feeling or energy; a tide; flood; period of intensity, usual activity, or the like; as, a wave of enthusiasm; waves of applause. [Webster 1913 Suppl.] Wave front (Physics), the surface of initial displacement of the particles in a medium, as a wave of vibration advances. Wave length (Physics), the space, reckoned in the direction of propagation, occupied by a complete wave or undulation, as of light, sound, etc.; the distance from a point or phase in a wave to the nearest point at which the same phase occurs. Wave line (Shipbuilding), a line of a vessel's hull, shaped in accordance with the wave-line system. Wave-line system, Wave-line theory (Shipbuilding), a system or theory of designing the lines of a vessel, which takes into consideration the length and shape of a wave which travels at a certain speed. Wave loaf, a loaf for a wave offering. --Lev. viii.
Wave moth (Zool.), any one of numerous species of small geometrid moths belonging to Acidalia and allied genera; -- so called from the wavelike color markings on the wings. Wave offering, an offering made in the Jewish services by waving the object, as a loaf of bread, toward the four cardinal points. --Num. xviii.
Wave of vibration (Physics), a wave which consists in, or is occasioned by, the production and transmission of a vibratory state from particle to particle through a body. Wave surface. (a) (Physics) A surface of simultaneous and equal displacement of the particles composing a wave of vibration. (b) (Geom.) A mathematical surface of the fourth order which, upon certain hypotheses, is the locus of a wave surface of light in the interior of crystals. It is used in explaining the phenomena of double refraction. See under Refraction. Wave theory. (Physics) See Undulatory theory, under Undulatory. [1913 Webster]
1 one of a series of ridges that moves across the surface of a liquid (especially across a large body of water) [syn: moving ridge]
2 a movement like that of an ocean wave; "a wave of settlers"; "troops advancing in waves"
3 (physics) a movement up and down or back and forth [syn: undulation]
4 something that rises rapidly; "a wave of emotion swept over him"; "there was a sudden wave of buying before the market closed"; "a wave of conservatism in the country led by the hard right"
6 a hairdo that creates undulations in the hair
7 an undulating curve [syn: undulation]
8 a persistent and widespread unusual weather condition (especially of unusual temperatures)
9 a member of the women's reserve of the United States Navy; originally organized during World War II but now no longer a separate branch
1 signal with the hands or nod; "She waved to her friends"; "He waved his hand hospitably" [syn: beckon]
3 move in a wavy pattern or with a rising and falling motion; "The curtains undulated"; "the waves rolled towards the beach" [syn: roll, undulate, flap]
4 twist or roll into coils or ringlets; "curl my hair, please" [syn: curl]
5 set waves in; "she asked the hairdresser to wave her hair"
Moby ThesaurusAfro, accost, address, advertise, affect, air, ambages, amplitude, anfractuosity, antinode, barber, be poised, beat, beat the drum, betoken, bicker, billow, blazon forth, bob, bobble, bore, bow, brandish, brandishing, break, breakers, breathe, bring forth, bring forward, bring into view, bring out, bring to notice, careen, chop, choppiness, chopping sea, circuitousness, circumambages, circumbendibus, circumlocution, circumvolution, coggle, coif, coiffure, cold wave, comb, comber, conk, convolution, crash, crest, crinkle, crinkling, curtsy, dance, dangle, dash, de Broglie wave, demonstrate, develop, diffraction, dip, dirty water, disclose, display, divulge, dramatize, eagre, ebb and flow, electromagnetic radiation, electromagnetic wave, emblazon, embody, embrace, enact, evidence, evince, exchange colors, exhibit, expose to view, express, flag, flag down, flap, flash, flaunt, flaunting, flexuosity, flexuousness, flick, flicker, flip, flit, flitter, float, flop, flourish, flourishing, fluctuate, flutter, fly, frequency, frequency band, frequency spectrum, give a signal, give sign, give the nod, give token, glance, go pitapat, gravity wave, greeting, ground swell, guided wave, gutter, hail, hail and speak, haircut, hairdo, hairstyle, half-mast, hand-clasp, handshake, headdress, heave, heavy sea, heavy swell, hello, highlight, hoist a banner, hold up, home permanent, how-do-you-do, hug, illuminate, in phase, incarnate, indicate, interference, intorsion, involution, kick, kiss, leer, librate, lift, light, longitudinal wave, lop, lurch, make a sign, make clear, make plain, manifest, materialize, mean, meander, meandering, mechanical wave, natural, nod, node, nudge, nutate, oscillate, out of phase, palpitate, parade, peak, pendulate, perform, period, periodic wave, permanent, permanent wave, pitch, pitter-patter, poke, pompadour, popple, present, process, produce, pulse, put forth, put forward, radio wave, raise a cry, ray, reel, reinforcement, represent, resonance, resonance frequency, resonate, reveal, riffle, ripple, rise, rise and fall, rivulation, rock, roll, roll out, roller, rough water, salutation, salute, scend, sea, seismic wave, send, set forth, shake, shaking, shingle, shock wave, show, show forth, sign, signal, signalize, sinuation, sinuosity, sinuousness, slat, slinkiness, smash, smile, smile of recognition, snakiness, sound an alarm, sound the trumpet, sound wave, speak, splutter, sport, spotlight, sputter, surf, surface wave, surge, swag, sway, swell, swing, swinging, throb, tidal bore, tidal wave, tide wave, token, torsion, tortility, tortuosity, tortuousness, toss, touch, transverse wave, trim, trot out, trough, trumpet, trumpet forth, tsunami, turning, twisting, undulate, undulation, unfold, unfurl a flag, vacillate, vaunt, vibrate, wag, waggle, water wave, wave a flag, wave equation, wave motion, wave number, wave the hand, wavelength, wavelet, waver, waving, white horses, whitecaps, wield, wigwag, winding, wink, wobble
Etymology 1Old English wafian, from Proto-Germanic *wab-, from Proto-Indo-European base *webh- "to move to and fro, to weave".
- To move back and
- The flag waved in the gentle breeze.
- To wave one’s hand in
greeting or departure.
- I waved goodbye from across the room.
- To have an undulating or wavy form.
- To swing and miss at a pitch.
- Jones waves at strike one.
- To cause to move back
and forth repeatedly.
- The starter waved the flag to begin the race.
- To signal someone or something with a waving movement.
move back and forth repeatedly'
wave one’s hand
- Arabic: (rafráfa)
- Bosnian: mahati
- Chinese: 招手 (zhāoshǒu)
- Croatian: mahati
- Dutch: zwaaien
- French: saluer
- German: winken
- Italian: agitare la mano
- Japanese: 振り動かす (ふりうごかす, furi ugokasu)
- Korean: 흔들다 (heundeulda)
- Norwegian: vinke
- Portuguese: acenar com a mão
- Russian: махать (maχát’)
- Spanish: hacer señal
- Swedish: vinka
- Telugu: ఊపు (oopu)
have an undulating or wavy form
- French: onduler
Etymology 2An alteration of waw, under influence of the verb; some senses developed directly from the verb.
- A moving disturbance in the level of
a body of water.
- The wave traveled from the center of the lake before breaking on the shore.
- A moving disturbance in the energy level of a field.
- A shape which alternately curves in opposite directions.
- Her hair had a nice wave to it.
- A sudden unusually large amount of something that is
- A wave of shoppers stampeded through the door when
the store opened for its Christmas discount special.
- A wave of retirees began moving to the coastal area.
- A wave of emotion overcame her when she thought about her son who was killed in battle.
- A wave of retirees began moving to the coastal area.
- A wave of shoppers stampeded through the door when the store opened for its Christmas discount special.
- A sideway movement of the hand(s).
- With a wave of the hand.
- Bosnian: talas, val
- Chinese: 波浪 (bōlàng)
- Croatian: val, talas
- Czech: vlna
- Danish: bølge
- Dutch: golf
- Estonian: laine
- Finnish: aalto (1-4)
- French: vague (1,4), onde (2), ondulation(s) (3)
- German: Welle (1-4)
- Greek: κύμα
- Hungarian: hullám
- Indonesian: gelombang
- Irish: tonn (1,4), italbrac of a hand croitheadh , italbrac hair casadh (3)
- Italian: onda
- Japanese: 波 (namí)
- Korean: 파도 (pado)
- Latin: unda
- Maltese: mewġa
- Norwegian: bølge
- Old English: ȳþ (1-3), wǣġ (1-3) g Old English
- Persian: (mowj)
- Portuguese: onda
- Proto-Polynesian: *peau
- Russian: волна
- Sanskrit: तरंग
- Spanish: onda
- Telugu: అల (ala) (1), తరంగం (taraMgaM) (2), కెరటం (keraTaM) (4)
- Turkish: dalga
- Tuvaluan: ngalu
- Zazaki: phêl
Etymology 3Variant forms.
- obsolete spelling of waive
A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium (which on deformation is capable of producing elastic restoring forces), waves of electromagnetic radiation (and probably gravitational radiation) can travel through vacuum, that is, without a medium. Waves travel and transfer energy from one point to another, often with little or no permanent displacement of the particles of the medium (that is, with little or no associated mass transport); instead there are oscillations around almost fixed positions.
DefinitionsAgreeing on a single, all-encompassing definition for the term wave is non-trivial. A vibration can be defined as a back-and-forth motion around a point m around a reference value. However, defining the necessary and sufficient characteristics that qualify a phenomenon to be called a wave is, at least, flexible. The term is often understood intuitively as the transport of disturbances in space, not associated with motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium (Hall, 1980: 8). However, this notion is problematic for a standing wave (for example, a wave on a string), where energy is moving in both directions equally, or for electromagnetic / light waves in a vacuum, where the concept of medium does not apply.
For such reasons, wave theory represents a peculiar branch of physics that is concerned with the properties of wave processes independently from their physical origin (Ostrovsky and Potapov, 1999). The peculiarity lies in the fact that this independence from physical origin is accompanied by a heavy reliance on origin when describing any specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a mechanical rather than an electromagnetic wave-like transfer / transformation of vibratory energy. Concepts such as mass, momentum, inertia, or elasticity, become therefore crucial in describing acoustic (as opposed to optic) wave processes. This difference in origin introduces certain wave characteristics particular to the properties of the medium involved (for example, in the case of air: vortices, radiation pressure, shock waves, etc., in the case of solids: Rayleigh waves, dispersion, etc., and so on).
Other properties, however, although they are usually described in an origin-specific manner, may be generalized to all waves. For example, based on the mechanical origin of acoustic waves there can be a moving disturbance in space-time if and only if the medium involved is neither infinitely stiff nor infinitely pliable. If all the parts making up a medium were rigidly bound, then they would all vibrate as one, with no delay in the transmission of the vibration and therefore no wave motion (or rather infinitely fast wave motion). On the other hand, if all the parts were independent, then there would not be any transmission of the vibration and again, no wave motion (or rather infinitely slow wave motion). Although the above statements are meaningless in the case of waves that do not require a medium, they reveal a characteristic that is relevant to all waves regardless of origin: within a wave, the phase of a vibration (that is, its position within the vibration cycle) is different for adjacent points in space because the vibration reaches these points at different times.
Similarly, wave processes revealed from the study of wave phenomena with origins different from that of sound waves can be equally significant to the understanding of sound phenomena. A relevant example is Young's principle of interference (Young, 1802, in Hunt, 1978: 132). This principle was first introduced in Young's study of light and, within some specific contexts (for example, scattering of sound by sound), is still a researched area in the study of sound.
Periodic waves are characterized by crests (highs) and troughs (lows), and may usually be categorized as either longitudinal or transverse. Transverse waves are those with vibrations perpendicular to the direction of the propagation of the wave; examples include waves on a string and electromagnetic waves. Longitudinal waves are those with vibrations parallel to the direction of the propagation of the wave; examples include most sound waves.
When an object bobs up and down on a ripple in a pond, it experiences an orbital trajectory because ripples are not simple transverse sinusoidal waves.
Ripples on the surface of a pond are actually a combination of transverse and longitudinal waves; therefore, the points on the surface follow orbital paths.
All waves have common behavior under a number of standard situations. All waves can experience the following:
- Reflection - wave direction change from hitting a reflective surface
- Refraction - wave direction change from entering a new medium
- Diffraction - bending of waves as they interact with obstacles in their path, most pronounced for wavelengths on the order of the diffracting object size
- Interference - superposition of two waves that come into contact with each other (collide)
- Dispersion - wave splitting up by frequency
- Rectilinear propagation - the movement of light waves in a straight line
PolarizationA wave is polarized if it can only oscillate in one direction. The polarization of a transverse wave describes the direction of oscillation, in the plane perpendicular to the direction of travel. Longitudinal waves such as sound waves do not exhibit polarization, because for these waves the direction of oscillation is along the direction of travel. A wave can be polarized by using a polarizing filter.
ExamplesExamples of waves include:
- Ocean surface waves, which are perturbations that propagate through water.
- Radio waves, microwaves, infrared rays, visible light, ultraviolet rays, x-rays, and gamma rays make up electromagnetic radiation. In this case, propagation is possible without a medium, through vacuum. These electromagnetic waves travel at 299,792,458 m/s in a vacuum.
- Sound — a mechanical wave that propagates through air, liquid or solids.
- waves of traffic (that is, propagation of different densities of motor vehicles, etc.) — these can be modelled as kinematic waves, as first presented by Sir M. J. Lighthill
- Seismic waves in earthquakes, of which there are three types, called S, P, and L.
- Gravitational waves, which are fluctuations in the curvature of spacetime predicted by general Relativity. These waves are nonlinear, and have yet to be observed empirically.
- Inertial waves, which occur in rotating fluids and are restored by the Coriolis effect.
Mathematical descriptionFrom a mathematical point of view, the most primitive (or fundamental) wave is harmonic (sinusoidal) wave which is described by the equation f(x,t) = A\sin(\omega t-kx)), where A is the amplitude of a wave - a measure of the maximum disturbance in the medium during one wave cycle (the maximum distance from the highest point of the crest to the equilibrium). In the illustration to the right, this is the maximum vertical distance between the baseline and the wave. The units of the amplitude depend on the type of wave — waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the electric field (volts/meter). The amplitude may be constant (in which case the wave is a c.w. or continuous wave), or may vary with time and/or position. The form of the variation of amplitude is called the envelope of the wave.
The wavelength (denoted as \lambda) is the distance between two sequential crests (or troughs). This generally is measured in meters; it is also commonly measured in nanometers for the optical part of the electromagnetic spectrum.
A wavenumber k can be associated with the wavelength by the relation
k = \frac. \,
The period T is the time for one complete cycle for an oscillation of a wave. The frequency f (also frequently denoted as \nu) is how many periods per unit time (for example one second) and is measured in hertz. These are related by:
In other words, the frequency and period of a wave are reciprocals of each other.
The angular frequency \omega represents the frequency in terms of radians per second. It is related to the frequency by
\omega = 2 \pi f = \frac. \,
There are two velocities that are associated with waves. The first is the phase velocity, which gives the rate at which the wave propagates, is given by
- v_p = \frac = f.
The second is the group velocity, which gives the velocity at which variations in the shape of the wave's amplitude propagate through space. This is the rate at which information can be transmitted by the wave. It is given by
v_g = \frac. \,
The wave equationThe wave equation is a differential equation that describes the evolution of a harmonic wave over time. The equation has slightly different forms depending on how the wave is transmitted, and the medium it is traveling through. Considering a one-dimensional wave that is traveling down a rope along the x-axis with velocity v and amplitude u (which generally depends on both x and t), the wave equation is
In three dimensions, this becomes
\frac\frac = \nabla^2 u. \,
where \nabla^2 is the Laplacian.
The velocity v will depend on both the type of wave and the medium through which it is being transmitted.
A general solution for the wave equation in one dimension was given by d'Alembert. It is
This can be viewed as two pulses traveling down the rope in opposite directions; F in the +x direction, and G in the −x direction. If we substitute for x above, replacing it with directions x, y, z, we then can describe a wave propagating in three dimensions.
The Schrödinger equation describes the wave-like behavior of particles in quantum mechanics. Solutions of this equation are wave functions which can be used to describe the probability density of a particle. Quantum mechanics also describes particle properties that other waves, such as light and sound, have on the atomic scale and below.
Traveling wavesSimple wave or a traveling wave, also sometimes called a progressive wave is a disturbance that varies both with time t and distance z in the following way:
y(z,t) = A(z, t)\sin (kz - \omega t + \phi), \,
where A(z,t) is the amplitude envelope of the wave, k is the wave number and \phi is the phase. The phase velocity vp of this wave is given by
v_p = \frac= \lambda f, \,
where \lambda is the wavelength of the wave.
Standing waveA standing wave, also known as a stationary wave, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions.
The sum of two counter-propagating waves (of equal amplitude and frequency) creates a standing wave. Standing waves commonly arise when a boundary blocks further propagation of the wave, thus causing wave reflection, and therefore introducing a counter-propagating wave. For example when a violin string is displaced, longitudinal waves propagate out to where the string is held in place at the bridge and the "nut", where upon the waves are reflected back. At the bridge and nut, the two opposed waves are in antiphase and cancel each other, producing a node. Halfway between two nodes there is an antinode, where the two counter-propagating waves enhance each other maximally. There is on average no net propagation of energy.
Propagation through stringsThe speed of a wave traveling along a vibrating string (v) is directly proportional to the square root of the tension (T) over the linear density (μ):
Transmission mediumThe medium that carries a wave is called a transmission medium. It can be classified into one or more of the following categories:
- A bounded medium if it is finite in extent, otherwise an unbounded medium.
- A linear medium if the amplitudes of different waves at any particular point in the medium can be added.
- A uniform medium if its physical properties are unchanged at different locations in space.
- An isotropic medium if its physical properties are the same in different directions.
- Campbell, M. and Greated, C. (1987). The Musician’s Guide to Acoustics. New York: Schirmer Books.
- Vibrations and Waves (M.I.T. Introductory physics series)
- Hall, D. E. (1980). Musical Acoustics: An Introduction. Belmont, California: Wadsworth Publishing Company.
- Hunt, F. V. (1978). Origins in Acoustics. New York: Acoustical Society of America Press, (1992).
- Ostrovsky, L. A. and Potapov, A. S. (1999). Modulated Waves, Theory and Applications. Baltimore: The Johns Hopkins University Press.
- Vassilakis, P.N. (2001). Perceptual and Physical Properties of Amplitude Fluctuation and their Musical Significance. Doctoral Dissertation. University of California, Los Angeles.
- A Radically Modern Approach to Introductory Physics - an online physics textbook that starts with waves rather than mechanics
- Interactive Visual Representation of Waves
- Science Aid: Wave properties - Concise guide aimed at teens
- Simulation of diffraction of water wave passing through a gap
- Simulation of interference of water waves
- Simulation of longitudinal traveling wave
- Simulation of stationary wave on a string
- Simulation of transverse traveling wave
- Sounds Amazing - AS and A-Level learning resource for sound and waves
- Vibrations and Waves - an online textbook
wave in Afrikaans: Golf (fisika)
wave in Arabic: موجة
wave in Official Aramaic (700-300 BCE): ܓܠܠܐ
wave in Azerbaijani: Dalğa
wave in Bulgarian: Вълна
wave in Catalan: Ona
wave in Welsh: Ton
wave in Danish: Bølge
wave in German: Welle (Physik)
wave in Modern Greek (1453-): Κύμα
wave in Esperanto: Ondo
wave in Spanish: Onda (física)
wave in Estonian: Laine
wave in Basque: Uhin
wave in Persian: موج
wave in Finnish: Aalto
wave in French: Onde
wave in Galician: Onda (física)
wave in Hebrew: גל
wave in Croatian: Val
wave in Hungarian: Hullám
wave in Indonesian: Gelombang
wave in Italian: Onda (fisica)
wave in Japanese: 波動
wave in Lojban: boxna
wave in Korean: 파동
wave in Kurdish: Pêl
wave in Lithuanian: Banga
wave in Latvian: Vilnis
wave in Malagasy: Onja
wave in Malay (macrolanguage): Gelombang
wave in Low German: Bülg
wave in Dutch: Golf (natuurkunde)
wave in Norwegian Nynorsk: Bølgje
wave in Polish: Fala
wave in Portuguese: Onda
wave in Romanian: Undă
wave in Russian: Волна
wave in Simple English: Wave (physics)
wave in Slovak: Vlnenie
wave in Slovenian: Valovanje
wave in Serbian: Талас (физика)
wave in Swedish: Mekaniska vågor
wave in Thai: คลื่น
wave in Turkish: Dalga
wave in Ukrainian: Хвиля
wave in Vietnamese: Chuyển động sóng
wave in Chinese: 波
wave in Contenese: 波