Something which can be described as having periodic motion, such as the motion of water in the ocean; waves tend to have the property of constructive and destructive interference, for example light of one wavelength may interfere with light of another wavelength to produce diffraction patterns...

W.A.V.E. is a very scary Nazi-like orginazation that is designed to spy on teenage geeks in high school. The general idea is that other kids are encouraged to call in if they see "suspicious" or "depressed" teens. The catch is that the accuser remains anonymous. I like the concept of someone who has a grudge on me to be able to ruin my life by seeking the W.A.V.E. secret police on me and tracking me for the rest of my life. *cringe*

Another amusing fact is that W.A.V.E. is a commercial organization! This means that they profit from spying on kids that are "different".

All this does is perpetuate the fear and hatred in our societ. It tells kids that if their peers aren't "normal", then they are violent and dangerous.


Here is a very probable scenario summarizing the problems that occur because of W.A.V.E.:

Lets say 2 kids get into a fight. One of them goes home and calls the W.A.V.E.'s toll-free, anonymous tip line. Lets say that they leave the tip that they overheard the other kid say he was going to kill himself. This kid that was turned in will most likely be brought down to the school's office to be questioned. The school administrators and councilors know that even if the kid did want to kill himself, he wouldn't openly admit it. If the kid happended to be abnormal or quiet to begin with, there would be a very good chance that the kid would be forced into treatment for his non-existant depression. In the meantime, the kid who turned him or her in would be laughing at his successful revenge while knowing that he will never be held responsible for his accusation.

Free, source-included Commodore 64 web browser that includes its own PPP stack. It runs on top of Wheels, the successor of GEOS, and utilizes SuperCPU.

So, how do you spot the Truly Elite Hackers now, those who take the Web to the very extreme??? Simple: See if this (or something similiar) shows up at the web server:

User-Agent: TheWave64/B2.7 Commodore64/CMD_SuperCPU


Sea Waves

The main factor in the formation of sea waves on the open ocean is wind. When winds blow across water, they apply a pressure due to friction, which pushes the water up, creating a wave. Within a wave, each water particle travels in a circular motion before returning to its original position. The wave will grow higher as long as the wind is strong enough to add energy. Once a wave is generated, it will travel in the same direction until it meets land or is dampened by an opposing force such as winds blowing against it. Once a wave moves away from the wind that generated it, it is called swell. Eventually this swell will flatten and broaden, but little or no energy is lost as it journeys across an ocean or sea. It is the surge of energy that moves rather than the individual water particles, rather in the manner of a longitudinal wave on a rope that is shaken, when it is the pulse not the rope fibres that move forward.

Waves can be classified into two main types, constructive and destructive. Constructive waves cause sediment to build up on beaches. They are most common when the fetch is large and the beach angle is gradual. The waves are flat and low, and their swash (the forward motion of the wave up the beach) is much stronger then their backwash (the backward motion of water returning from a previous wave). Sediment builds up slowly on the shore because only six to eight waves break on the shore every minute. Destructive waves help to remove sediment from beaches. They are more common when the fetch is short and the beach angle steep. The waves are steep and high, with a stronger backwash than swash. This allows the ten to fourteen waves breaking every minute to drag sediment offshore.


In the first chapter of his extraordinary Lectures on Physics, Richard Feynman presents his belief that the sentence "All things are made of atoms" contains more information per word than any other. I believe that the word atoms should be replaced with the word waves. The wave is ubiquitous in the applied sciences, and an argument could be made that it is the most fundamental concept in physics. I hope to convince you of the importance of waves and to help you better understand wave-related fields of science.

The importance of waves to applied science

The study of sound waves in air is useful to musicians, musical equipment manufacturers (both acoustic and electric), architects, and biologists and psychologists who wish to understand human perception. Sound waves in liquid or solid (in which case they are called phonons) media are important to scientists who study electronic devices, the communication of dolphins, SONAR, etc.

Water waves (which aren't too dissimilar from sound waves) are very important in the fields of oceanography and coastal engineering. Seismic waves (essentially sound waves in the earth) are obviously of considerable interest to geologists.

The study of electromagnetic waves is vital to scientists in such fields as optical communication, photolithography, satellite communication, portable electronics, lasers, optical lenses, radar, perception, x-ray imaging, and x-ray crystallography (I could continue for a long time).

I also want to note that the wave-nature of matter has become important to chemists, materials scientists, electrical engineers, and generally anyone who works in an area in which atomic-level understanding is required. There are many other types of waves with which I am less familiar.

The importance of waves to fundamental physics

As far as we know, everything in the universe--matter and energy--is a wave. Recently someone submitted a writeup on gravity waves (a predicted but still unobserved phenomenon) which might be of interest to you. It is often said that the universe has a wave/particle duality, meaning that everything in the universe has both wave and particle characteristics. While this is true, it is interesting to note that a particle (i.e. a precisely localized object) can be visualized as an infinite sum (integral) of waves. In mathematical terms, the Fourier transform of the Dirac delta function* is just 1. This fact implies that the delta function is a sum of equally-weighted sinusoids of all frequencies.

* The Dirac delta function is the limit of a set of functions normalized to 1 as their bandwidth approaches 0. Think of a bell curve (Gaussian) centered around the point X as an example. Since the bell curve represents probability density, its integral over all space is 1. Imagine squeezing the bell curve so that its spread gets smaller and smaller, and its peak gets higher and higher to preserve probability. In the limit of squeezing, the peak is "infinity" and the spread about X is 0. This is the delta function. A function (actually to mathematicians this isn't a true function) defined in such a limit is called a generalized function.

What is a wave?

This is a most difficult section for me! Waves are present in so many forms and contexts that it is difficult to isolate the underlying property that makes them "waves." I will define a wave in a rather technical way. It gets easier from here. A wave is a function of space and time that can be written as a superposition of basis functions of the form

Akcos(kz - w(k)t + φ(k)).

φ(k) is called the phase of a basis wave. k is called a wavevector (though we will work in one-dimension so we might call it a wavenumber). w is known as the angular frequency of a basis wave. t is time and z is a direction in space. Ak is just a weighting coefficient.

Let's look at the term in the parentheses--(kz - w(k)t + φ(k)). At a particular time t and a particular point z the term has some value which we can call C. Notice that If we increase t a little bit (i.e. we let time elapse), we can increase z a little bit to keep the value of the term at C. How much do we have to increase z to keep a constant C? Well, kz - w(k)t + φ(k) = C. So kz - w(k)t is a constant D. That means z = D + (w(k)/k)t and dz/dt = w(k)/k. This is the speed of the wave! Every point on the basis wave travels at this same speed since C was arbitrary.

Usually waves with different angular frequencies w move with the same speed, which we'll call c. However, waves can move in any direction. In the one-dimensional case that we'll consider, this means that dz/dt = +/- c. If dz/dt = +c, the wave is moving rightward along the z-axis. If dz/dt = -c, the wave is moving leftward. We see that w(k)/k = +/- c implies that w(k) = +/- ck--it's just a linear function of k. The reader should realize that dispersion, an effect in which waves with different angular frequencies travel with different speeds, is very critical in many fields. For example, the amount of information that can be transmitted through optical fibers is governed by dispersion.

w(k) has the units of radians/second. 2π radians = 360 degrees. If we look at what happens at a single point z, we see a full oscillation every time w(k)Δt = 2π. Δt is known as the period of the wave. It is equivalent to 2π/w. Notice that there are 1/Δt oscillations per second. The number of oscillations per second is called the frequency (different from angular frequency). The frequency and angular frequency are related by f = w/2π.

There are some other things to note. I assumed that all waves propagate along the z-axis. This is fine for the purposes of understanding basic wave behavior, but one should know that in three dimensions, k is a vector and z is replaced by the position vector r. The polarization of some waves (such as electromagnetic waves) is not critical to understanding waves, but it can be included by making the coefficients Ak vectors. For quantum mechanical purposes, the coefficients Ak are complex numbers.

Superposition/interference of waves

In general, a wave is a sum of the basis waves described above. This sum can be quite complicated--the resultant wave can look nothing like a sinusoid! It is important to realize that implicitly, we are assuming that waves simply add linearly. In other words, if two waves intersect eachother, we can treat them as one wave which is a simple addition of the two waves. This is almost always a valid assumption, but there are nonlinear phenomena that can have interesting effects. We won't discuss them here but you should be aware that the field of nonlinear optics has become fairly important.

So imagine a "wave" that is a sum of two basis waves that are identical in every respect except that one of the phases is 180 degrees (or π radians) away from the other. From basic trigonometry, a sine wave with a constant phase of (180 + x) degrees is just the negative of a sine wave with phase x. Thus the sum of the two basis waves is zero! This situation is called destructive interference. When two waves that are 180 degrees out-of-phase come together at some point, they disappear. Of course, if the phase difference between the two waves is 0 degrees, then the resultant wave is just the simple sum of the two. This situation is called constructive interference. Everything between complete constructive interference and complete destructive interference is possible. The constructive and destructive interference of waves are responsible for many phenomena such as beats and wavepackets.

More information about waves

Originally I intended to discuss several wave phenomena in this writeup. However, it is fairly long as it is, and to this point it has been a review of the very basics of waves, which might not be useful to all scientists. I will link this node to other nodes in which I plan to add future writeups. Actually, on further thought I'm not going to waste my time making these writeups that nobody reads and nobody respects. One or the other would make it worth my while. And since I'm not interested in milkshakes, tv, or penises, this is adieu.

Do The Wave: A Staple Form of Audience Participation at Sports Arenas Around the World

This phenomenon of adjoining sections of spectators standing up, raising their arms, and sitting back down in sequence, thus creating a wavelike appearance, is of recent origin. It suddenly appeared during a football (American style) game one day in 1981, and caught on like wildfire. The man with the best claim of inventing it is George Henderson, A.k.a "Kraaazy George." Krazy George is a professional cheerleader (yet not officially attached to any of the teams). He can be seen at NFL games in Houston and Minnesota banging his drums and harassing the other teams. On Oct. 15th, 1981, he was workin a playoff game between the Yankees and the Oakland A's in Oakland Coliseum. Midway through the game, he had a now famous inspiration. He went from section to section asking them to standup, yell, and sit down. The first time, only a few sections complied, then seven more, and by the third attempt the wave went right around the stadium and continued. The sports announcers talked it up, and within weeks, it was in every sport stadium around the country.

Mr. Nolan, my US History and Government teacher. (Quite a cool guy!)
Facts double-checked with Encarta and The Trivia Handbook, by Tom Lowes.

Wave (?), v. t.

See Wave.

Sir H. Wotton. Burke.


© Webster 1913.

Wave, v. i. [imp. & p. p. Waved (?); p. pr. & vb. n. Waving.] [OE. waven, AS. wafian to waver, to hesitate, to wonder; akin to waefre wavering, restless, MHG. wabern to be in motion, Icel. vafra to hover about; cf. Icel. vafa to vibrate. Cf. Waft, Waver.]


To play loosely; to move like a wave, one way and the other; to float; to flutter; to undulate.

His purple robes waved careless to the winds. Trumbull.

Where the flags of three nations has successively waved. Hawthorne.


To be moved to and fro as a signal.

B. Jonson.


To fluctuate; to waver; to be in an unsettled state; to vacillate.


He waved indifferently 'twixt doing them neither good nor harm. Shak.


© Webster 1913.

Wave, v. t.


To move one way and the other; to brandish.

"[Aeneas] waved his fatal sword."



To raise into inequalities of surface; to give an undulating form a surface to.

Horns whelked and waved like the enridged sea. Shak.


To move like a wave, or by floating; to waft.


Sir T. Browne.


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.

Look, with what courteous action It waves you to a more removed ground. Shak.

She spoke, and bowing waved Dismissal. Tennyson.


© Webster 1913.

Wave, n. [From Wave, v.; not the same word as OE. wawe, waghe, a wave, which is akin to E. wag to move. . See Wave, v. i.]


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.

The wave behind impels the wave before. Pope.

2. 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.


Water; a body of water.

[Poetic] "Deep drank Lord Marmion of the wave."

Sir W. Scott.

Build a ship to save thee from the flood, I 'll furnish thee with fresh wave, bread, and wine. Chapman.


Unevenness; inequality of surface.

Sir I. Newton.


A waving or undulating motion; a signal made with the hand, a flag, etc.


The undulating line or streak of luster on cloth watered, or calendered, or on damask steel.


Fig.: A swelling or excitement of thought, feeling, or energy; a tide; as, waves of enthusiasm.

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. 27. -- 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. 11. -- 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.


© Webster 1913.

Wave (?), n. [See Woe.]




© Webster 1913.

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