What is the definition of wave?

[Geolay]

Which is the most important nature of wave? period? energy? or other?

thanks

[HallsofIvy]

The crucial point, in my opinion, is that a wave transports energy from place to place without transporting matter (or whatever it is that the wave is "waving" in).

[Academic]

Ive think of a wave a that which satisfies the wave equation.

[Geolay]

Ive think of a wave a that which satisfies the wave equation.

So what is the crucial point of a wave equation? I think your answer follows no logic.

[Mu naught]

So what is the crucial point of a wave equation? I think your answer follows no logic.

His definition is circular. I would pay attention to what Hallofivy said.

[stevenb]

The crucial point, in my opinion, is that a wave transports energy from place to place without transporting matter (or whatever it is that the wave is "waving" in).

What about standing waves?

Also, nonlinear effects in ocean waves allow water to be transported as well as energy.

Many things in science are not easy to define. For example "life" is a classic example.

[sophiecentaur]

Standing waves can be described in terms of a series of progressive waves travelling in different directions. The energy ends up being stored rather than being transported.

A fairly catch=all description of a wave could be a disturbance that travels through space. (That allows for the need for some waves to have a medium to travel through)

[stevenb]

A fairly catch=all description of a wave could be a disturbance that travels through space. (That allows for the need for some waves to have a medium to travel through)

A boulder rolling down a hill is a disturbance that travels through space, but it is not a wave, or is not usually thought to be so. (no comments about DeBroglie wavelength please)

[Academic]

So what is the crucial point of a wave equation? I think your answer follows no logic.

Crucial point? The wave equation is defined as a second time derivative equal to a second spatial derivative, with a constant factor. Any solution to that equation is a wave and the constant factor is proportional to the speed of that wave. If a phenomenon can be described by that solution to the wave equation, then it is considered a wave.

[sophiecentaur]

A boulder rolling down a hill is a disturbance that travels through space, but it is not a wave, or is not usually thought to be so. (no comments about DeBroglie wavelength please)

Yebbut it's primarily a boulder moving. It's causing a disturbance and actually setting up a wave as it goes, because it is causing havoc and moving things as it goes. In a very lossy medium a wave won't propagate unless you keep supplying energy all the time.
Perhaps I should have added something about nothing actually being permanently displaced.
Edit-
I seem to remember a wave being described in the general form of

A =A0 Fn(px-qt)
Where A is some some generalised displacement and Fn is some periodic function of x and t.

[dulrich]

Last year I spent quite a bit of time trying to formulate a definition of wave motion that is equally applicable to strings, springs (like a slinky), air, light, and de Broglie waves. This is the best I've got:

A wave requires a source and a medium made up of coupled oscillators near equilibrium. Any initial disturbance in the medium caused by the source will act as a damped oscillator as its energy radiates away in the medium. In order to support a sustained disturbance, the source must continually add energy to drive the oscillation.

It's still a bit wordy, but I wanted to incorporate several elements:


A wave occurs in a medium. It is the medium which governs the nature of the wave (via the wave equation). The medium also controls the types of polarization available to the wave.
A wave is a type of radiation: it carries energy from the source to the observer without transporting mass. The impedance of the radiation is also controled by the medium.
A wave needn't be a pure easy-to-draw 1D sine wave. Ripples in a pond, atomic orbitals are also imporantant solutions to the wave equation.
The type of source also plays an important role. Plucking a guitar string and a dipole antenna produce very different radiation patterns within their media.
The source controls the frequency and the medium controls the speed (which may be dispersive).

[billiards]

I strongly recommend giving this Nature article a read:

"What is a wave?"
http://inside.mines.edu/~rsnieder/nature_wave.pdf (pdf file -- 66 KB)

The author's conclude:


It is striking that the concept of waves is
so hard to define, and that the distinction
between wave-like and non-wave-like behaviour
can be so fuzzy. Taking all these examples
into account, we stick with our definition of a
wave as an organized propagating imbalance;
just don’t ask us to define ‘organized’.

[sophiecentaur]

"an organised propagating imbalance" sounds as good as anything I've read. (Last line of that article).

[dulrich]

I strongly recommend giving this Nature article a read:

"What is a wave?"
http://inside.mines.edu/~rsnieder/nature_wave.pdf (pdf file -- 66 KB)

That's a great article. Thanks.

[Geolay]

I strongly recommend giving this Nature article a read:

"What is a wave?"
http://inside.mines.edu/~rsnieder/nature_wave.pdf (pdf file -- 66 KB)

The author's conclude:

Thank u for this article!

[billiards]

That's a great article. Thanks.

Thank u for this article!

You're welcome

[stevenb]

"an organised propagating imbalance" sounds as good as anything I've read. (Last line of that article).

Personally, I don't like this definition at all. It is useless to someone who understands waves already, and it is confusing to someone who is trying to learn what a wave is.

The words organised and imbalance are not well defined or clear in physics. The word "organized" relates to entropy which just confuses the question even more, and "imbalance" seems to imply force, but is still vague. Also, standing waves do not propagate.

I think we could do better here if we set our minds to it. Personally, I thought Hallsof Ivy was off to a good start when he said.

"a wave transports energy from place to place without transporting matter (or whatever it is that the wave is "waving" in)"

That would certainly get a beginning student off to a better start than what the article proposes (half-seriously).

I mentioned issues with the above quoted definition (specifically standing waves and transportation of matter, and there are many more). I did this to bring up the point that definition of a "wave" is difficult, and at best one can obtain a good description or a useful circular definition, as is often the case in science.

Remember that biologists can't even define life clearly, yet every person knows what it is. Similarly, we can have a description of waves that allow anyone to know a wave when they see it. The article does provide that good description, but the proposed "definition" does not. How would a new student not interpret a boulder rolling down the hill as an "organized propagating imbalance"? Would he say it is not "organized" enough to be a wave? Otherwise, it is propagating and not balanced. At least the desciption from HallofIvy tells the student the boulder is not a wave because it is propagating matter. Even the description that a wave is a "solution to the wave equation" can help eliminate the boulder as being a wave.

Basically, I don't have the answer to an unanswerable question, but the group here at PF is as qualified as any other to come up with an operational definition that's better than the quoted article, ... although it is a good article - don't get me wrong. Also, I do agree with the main point of the article; namely that it is difficult to define what a wave is.

[Studiot]

Firstly should we differentiate between continuous and discrete periodic phenomenon?

We can only talk about derivatives if we restrict our definition to continuous phenomena.

If we allow discrete, what about modulo arithmetic, Brillouin Zones etc? They are periodic phenomena - do we count them as waves?

One characteristic (not in the PDE sense) is the difference between a wave and say an exponential - The wave, being a plot of some desired variable against some baseline (usually time), remains bounded by curving or curling back on itself repeatedly.