What is a Wave? Explaining the Basics of Wave Phenomena

[craig1888]

Well this will hopefully be in answered in one post since I think it's supposed to be simple.
What exactly is a wave and a wave function?
I tried looking at the wiki but it kept mentioning things i didn't know so i ended up on a completely unrelated page after following all sorts of links.

As you can tell I've never done any form of physics so please try and explain it very simply.
I do like coming on here and just looking at some threads and i sometimes pick up on the more basic stuff people explain:P

 

[noblegas]

a wavefunction is comparable to Newton's equations in that just as Newton's laws describe the behavior of a physical system using a deterministic approach, meaning you can exactly determned the position of an object upon precise measurment, a wavefunction would describe a physical system evolving with time and the physical system is indeterministic probabilities and only applies to the atomic and subatomic realm of a physical system. For example , when you measure the position of an electron, their is a chance that when you attempt to measure the position of the electron, it will not be in the same position that it was previously in. A wave is one of the two physical properties that a particle, the other property being a particle, can exhibit interference.I suppose I should say that an electron in certain circumstances, can exhibit an particle like properties and in other circumstances, an electron can exhibit a wavelike property and you know when an electron exhibits wave like properties when it projects interferene patterns. Usually when a bunch of electron projected into two slits, you start to see an interference pattern and notice its wave properties.

 

[Frame Dragger]

Just to clarify what an actual 'wave' is, not a wavefunction: Imagine an ocean of billiard balls. You drop a bus into the ocean, and disturb a hell of a lot of balls, right? Well, we know that the balls from where you dropped the bus are not the balls that carry the wave... they don't move too much. Instead, they impact and transfer energy (momentum) to their neighbours. The propogation (movement away from the source) of this wave is just those balls nudging the next in line (like a slinky spring). The wave itself, is the energy which propogates through the displacement of the balls.

In real life, we have oceans of billiard balls called atoms (from a macroscopic point of view).

The wavefunction is totally different. As nobelgas said, is the plotted probablity of finding (say, an electron in a hydrogen atom) in any given "spot". Because of the nature of Quantum Physics (you may have heard of Heisenberg's Uncertainty Principle 'the HUP'), we don't get to play with billiard balls, but only probabilities.

The effect of wave-particle duality, or a wavefunction, or a pilot wave (whatever you believe) among many other thing is that as a result of the mathematics of waves, when particles pass through the classic double slit, they create interfernece patterns (look up young double slit test for examples) such as Noblegas mentioned. In the standard formulation of Quantum Physics particles act as particles AND waves, but never so that both properties can be simultaneously observed.

 

[Naty1]

One way to picture a wave is a water wave..driven by wind, or emanting outward after a rock is thrown...so you can see they take different forms even in a single media...

Wikipedia says:

A wave function or wavefunction is a mathematical tool used in quantum mechanics to describe the momentary states of subatomic particles.

It is a function from a space that maps the possible states of the system into the complex numbers. The laws of quantum mechanics (i.e. the Schrödinger equation) describe how the wave function evolves over time. The values of the wave function are probability amplitudes — complex numbers — the squares of the absolute values of which give the probability distribution that the system will be in any of the possible states.

You can get other perspectives by looking up sound waves and light waves...longitudional and transverse types.

A simple mathenmatical wave would be a sine or cosine function...by combining these together in different patterns you can mimic other 'waves' like a step function or a square wave function in electronic circuits...Fourier tranforms and Laplace transforms are mathematical formulations which can be used to approximate such forms...

 

[billiards]

"a wave is an organized propagating imbalance"

http://inside.mines.edu/~rsnieder/nature_wave.pdf

 

[luxiaolei]

Wave is not ''something'', wave is form of energy transform. say a water wave, the water does NOT move in the direction of the wave, the energy moves.

Wavefunction is something contain all infomation of one object, and you might ask, why is ''wave''function rather than ''function'' only, well, because after we observe the world and found certain constrains, then we put these constrains into a equation, and the solution to that equation can only be the form of ''wave''.

 

[elibj123]

A classical wave (light-wave, sound-wave) is a field attaching a set of numbers to each point in space. For a sound-wave it would be the density of air/another gas in a point. For a light-wave it would be the intensity of light which is a scalar, or far more informative- the Electromagnetic field (which are 6 numbers) at a certain point.

In quantum mechanics, a particle in a certain system, is attahced with a wavefunction which is derived from the Schroedinger Equation. The wavefunction is still a field (although complex now), but it has a different interpertation- the absolute value of the field squared, is the probabillity density of finding the particle at a certain point.

Waves obey wave equations just like a particle (or more accuratly his position function x(t) ) obeys motion equations (in classic mechanics, that would be the Newtonian equations, or Euler-Lagrange Equations or The Hamilton Equations, which are all equivalent). But because waves exhibit a spatial variance, in addition to the temporal one, their equations of motion will be Partial Differential Equations, and more complicated to solve. The most common and basic wave equation is:

$$\partial_{tt}\psi=c^{2}\nabla ^{2} \psi$$

Which can describe the propagation of light in vaccum.

A more complicated one is the Schroedinger equation:

$$i\hbar \partial_{t}\psi=-\frac{\hbar ^{2}}{2m}\nabla ^{2} \psi+V(\vec{r})\psi$$

For a qunatum particle in a potential V(x,y,z).

 

[Gear300]

A wave is an energy field (this definition might be oversimplified, but I think it works).

 

[Frame Dragger]

A classical wave (light-wave, sound-wave) is a field attaching a set of numbers to each point in space. For a sound-wave it would be the density of air/another gas in a point. For a light-wave it would be the intensity of light which is a scalar, or far more informative- the Electromagnetic field (which are 6 numbers) at a certain point.

In quantum mechanics, a particle in a certain system, is attahced with a wavefunction which is derived from the Schroedinger Equation. The wavefunction is still a field (although complex now), but it has a different interpertation- the absolute value of the field squared, is the probabillity density of finding the particle at a certain point.

Waves obey wave equations just like a particle (or more accuratly his position function x(t) ) obeys motion equations (in classic mechanics, that would be the Newtonian equations, or Euler-Lagrange Equations or The Hamilton Equations, which are all equivalent). But because waves exhibit a spatial variance, in addition to the temporal one, their equations of motion will be Partial Differential Equations, and more complicated to solve. The most common and basic wave equation is:

$$\partial_{tt}\psi=c^{2}\nabla ^{2} \psi$$

Which can describe the propagation of light in vaccum.

A more complicated one is the Schroedinger equation:

$$i\hbar \partial_{t}\psi=-\frac{\hbar ^{2}}{2m}\nabla ^{2} \psi+V(\vec{r})\psi$$

For a qunatum particle in a potential V(x,y,z).

The OP said, and I quote, "As you can tell I've never done any form of physics so please try and explain it very simply."

I think that might include things like the particulars of notations, such as what "Psi" is, or what the reduced Planck's constant is. I see nothing wrong with including that level of information, but if you do, walk him through it to that point.

 

[threadmark]

A periodic disturbance of particles in a substance which may be propagated without net movement of the particles, as in the passage of undulated motion or sound.

 

[craig1888]

Thanks for all the replies everyone, i get it now. I was pretty much getting confused because i thought a wave and a wave function were the same but it makes sense now.
Thanks again:)

 

[Studiot]

At an introductory level some key points about waves.

Waves generally require some medium in which to propagate. This can be air, water a solid and so on. Light 'waves' are a special case as light also has non wave properties.

Waves can be one dimensional as in a stretched string
two dimensional as in a drumskin
three dimensional as is the sound in the air emitted by the drum or stretched string.
Normally three dimensional waves can be polarised. That means they are constrained to two or even one dimension.

If the medium is material the wave is generated by motion of the particles of the medium. The particles repeatedly make the same motion. This motion is distinct from the wave itself.
If the medium is non material the wave is generated by variation of some property of that medium. Again the wave is distinct from the property.
This motion or variation can be in the same direction as the motion of the wave in which case we call the wave a longitudinal wave.
Alternatively it can be at right angles to the motion of the wave in which case we call the wave a transverse wave.
Sound is a longitudinal wave, light is a transverse wave.

Waves can be standing (stationary) or travelling.

Since a wave comprises motion of the constituent particles of its medium two (or more) waves can affect each other. Each wave tries to move the particle in its own way and the resultant movement is called interference.

 

[sophiecentaur]

I can't find the word 'perturbation' in this thread.
I should have thought that a sentence like
'A wave is the transference of a perturbation through a medium.'
might be a suitable, non-specific, description - although waves will also be associated with the transfer of energy. I'm not sure where a 'Mexican Wave' fits in here.