Understanding Waves: Is There Hope?

[Misr]

Hello World,
These days, I'm trying to introduce the concept of waves into my stupid mind but It seems to be Hopeless..Whatever..
What are waves really?Can we see waves by any means in the world ?or they just do disturbance to the medium particles?

Is there a real hope to understand waves?

Thanks

 

[SteamKing]

Have you ever dropped a pebble into a pond? Those ringey things on the surface traveling away from where the pebble went in are waves.

 

[Renaatier]

Hello World,
These days, I'm trying to introduce the concept of waves into my stupid mind but It seems to be Hopeless..Whatever..
What are waves really?Can we see waves by any means in the world ?or they just do disturbance to the medium particles?

Is there a real hope to understand waves?

Thanks

The wave-like properties of light and other elementary particles can be observed through the double-slit experiment. Youtube search double-slit experiment. Unfortunately, Physicists even today cannot agree as to whether photons and other quantum particles create the wave, ride a preexisting wave, or simply just follow a wave-like path since that is the nature of all movement. Physics today is a mess of conflicting theories and paradoxes, and it all comes back to wave-particle duality. Once you get into physics and you hear things like "quantum weirdness"--you know they're hopelessly lost, if they're just saying "man that's weird" out loud.

 

[Misr]

Have you ever dropped a pebble into a pond? Those ringey things on the surface traveling away from where the pebble went in are waves.

so we can see waves according to you?

The wave-like properties of light and other elementary particles can be observed through the double-slit experiment. Youtube search double-slit experiment. Unfortunately, Physicists even today cannot agree as to whether photons and other quantum particles create the wave, ride a preexisting wave, or simply just follow a wave-like path since that is the nature of all movement. Physics today is a mess of conflicting theories and paradoxes, and it all comes back to wave-particle duality. Once you get into physics and you hear things like "quantum weirdness"--you know they're hopelessly lost, if they're just saying "man that's weird" out loud.

my question is quite simple and I think i can't get the answer that satisfies my eagerness

thanks

 

[Misr]

http://www.school-for-champions.com/science/images/waves-wavelength.gif
What does this represent?Don't tell me a wave..Does this represent the vibrations of particles of the medium? If so then what is a wave?Can this wave be seen?? Answer me

 

[Dale]

my question is quite simple

In one clear and unambiguous sentence, what is your simple question?

 

[Misr]

In one clear and unambiguous sentence, what is your simple question?

Well,sorry,It's not one question..it's a combination of many questions , i can't introduce the concept of a wave into my mind and I'm suffering a lot ..
First of all :Can we see waves by any means in the world ?or they just do disturbance to the medium particles?
http://www.school-for-champions.com/...wavelength.gif
What does this represent?Don't tell me a wave..Does this represent the vibrations of particles of the medium? If so then what is a wave?Can this wave be seen??

Thanks in advance

 

[Dale]

Well,sorry,It's not one question..it's a combination of many questions

Then it is a little unfair for you to respond to Renaatier as you did.

, i can't introduce the concept of a wave into my mind and I'm suffering a lot ..
First of all :Can we see waves by any means in the world ?or they just do disturbance to the medium particles?
http://www.school-for-champions.com/...wavelength.gif
What does this represent?Don't tell me a wave..Does this represent the vibrations of particles of the medium? If so then what is a wave?Can this wave be seen??

In physics, a good definition of a wave is any phenomenon which behaves according to the wave equation:
http://en.wikipedia.org/wiki/Wave_equation

There are many different systems that behave according to the wave equation, so yes, we see waves by many means in the world. Some waves are disturbances to some medium of particles, but others are disturbances to fields. It doesn't really matter what the function (u in the Wikipedia article) represents, only how it behaves.

 

[Misr]

hmmm so we see water waves?these circles are called water waves then?

 

[Misr]

In physics, a good definition of a wave is any phenomenon which behaves according to the wave equation:

but the wave equation is very complicated for me and we don't study these things at school>>are there any simpler ways?

 

[VortexLattice]

It depends on the type of wave. In water, the shape of the wave shows where the water is physically higher. That's the one you're used to.

With light, it represents the strength of the electric field at that point. In quantum mechanics, it represents where something is likely to be found. Waves can mean many things depending on the context!

 

[Dale]

but the wave equation is very complicated for me and we don't study these things at school>>are there any simpler ways?

There are certainly simpler ways to understand specific kinds of waves, but to understand the general underlying phenomenon I think requires the math. Is there a specific kind of wave that you are interested in for simplicity's sake? If so, then we can probably discuss that specific kind of wave without a lot of equations.

 

[Misr]

There are certainly simpler ways to understand specific kinds of waves, but to understand the general underlying phenomenon I think requires the math. Is there a specific kind of wave that you are interested in for simplicity's sake? If so, then we can probably discuss that specific kind of wave without a lot of equations.

ok,let's talk about water waves and sound waves

 

[Dale]

Let's start with sound waves. In a sound wave we are looking at small spatial and temporal deviations in the air pressure and velocity from the "bulk" pressure and velocity.

If you consider a small chunk of air then if the pressure on the left is greater than the pressure on the right there will be a net force on the chunk which will cause it to accelerate to the right. In doing so it will get closer to the neighboring chunk on the right and further away from the neighboring chunk on the left. This will cause the pressure on the right to increase and the pressure on the left to decrease, bringing both back to equilibrium.

However, by the time that the pressure equalizes the chunk of air will have gained some velocity to the right, and due to its natural inertia will continue move in that direction. This will cause the pressure on the right to continue to increase and the pressure on the left to continue to decrease, beyond the equilibrium value.

As this continues the chunk of air exeperiences a net force to the left, which works to decelerate the chunk of air. As the difference in pressure to the left and right increases, the deceleration increases, until finally the chunk of air is brought to a stop.

At this point the chunk of air is stationary with the pressure on the right being greater than the pressure on the left. The situation then repeats in reverse, each oscillation going through this cycle.

 

[Misr]

Yes,this seems clear..I'm starting to draw a clear picture right now.and a tuning fork is a good example of this (it affects the pressure) right?
Thanks very much for this clear explanation and now I can ask some more clear and definite questions:
1-Why do sound travel through solids faster than liquids faster than gases??I think it has somethin to do with the intermolecular forces.

2-why do longtudinal waves travel in gases only?I think it has somethin to do with the intermolecular forces too.
3-the waves of the surface of a cup of water are transeverse while in depth,there exist longitudinal; waves..so why?

4-on tossing a stone in a pond..why do we consider the postition of the stone as the first crest??what is the wave length then?where are crests and troughs in this case..
I can't deal with these kinds of problems..It would be great if you use some illustrations

Thanks very much..

 

[olivermsun]

In physics, a good definition of a wave is any phenomenon which behaves according to the wave equation:
http://en.wikipedia.org/wiki/Wave_equation

As Whitham (1974) pointed out, many (if not most) waves are not governed by the "wave equation"!

(He gives a much broader definition, that a wave is "a recognizable signal that is transferred from one part of a medium to another with a recognizable velocity of propagation.")

 

[Naty1]

What are waves really?Can we see waves by any means in the world ?or they just do disturbance to the medium particles?

Try reading some here:

http://en.wikipedia.org/wiki/Waves

and look at the illustrations and explanations under each.

You can also look up TRANSVERSE WAVE AND LONGITUDIONAL WAVE if interested.


Waves in general carry energy ( a disturbance) from one place to another. It turns out some waves required a medium, like water waves, and others don't, like light (an electromagnetic wave). Sometimes you can see them (by eye) sometimes not. For example you can see light (waves) from the sun but not higher frequency waves from an X-ray machine.

 

[Dale]

1-Why do sound travel through solids faster than liquids faster than gases??I think it has somethin to do with the intermolecular forces.

Yes, the intermolecular forces are given by Young's modulus (stiffness), the stiffer the material the faster the speed of sound. The other thing that affects the speed of sound in a material is the density of the material, the lighter the material the faster the speed of sound.

2-why do longtudinal waves travel in gases only?I think it has somethin to do with the intermolecular forces too.

Longitudinal waves travel in liquids and solids also. Since a fluid deforms under shear stress it is very hard to get transverse waves in a fluid.

3-the waves of the surface of a cup of water are transeverse while in depth,there exist longitudinal; waves..so why?

I don't think this is correct. Do you have a reference?

4-on tossing a stone in a pond..why do we consider the postition of the stone as the first crest??what is the wave length then?where are crests and troughs in this case..

The definition of wavelength is unchanged, the crests are the tops of the ripples and the troughs are the bottoms of the ripples. I suspect I am not understanding what you are actually asking.

 

[Misr]

I don't think this is correct. Do you have a reference?

our textbook of physics :(

 

[John15]

Re electromagnetic waves. They have length and amplitude but do they have width or what would they look like end on? Waves on water are obviously 3d because the medium they propagate through is 3d. How can a massless wave be 3d.

 

[Dale]

The wave equation for EM involves 3 dimensions of space and 1 dimension of time, so I would say it is 4D. I don't know what mass has to do with it.

 

[nitsuj]

The wave equation for EM involves 3 dimensions of space and 1 dimension of time, so I would say it is 4D. I don't know what mass has to do with it.

is position in those 3D's definitive? Or a probability of where it is?

 

[Dale]

Depends if you are doing classical EM (Maxwell's equations) or quantum EM (QED).

 

[nitsuj]

Depends if you are doing classical EM (Maxwell's equations) or quantum EM (QED).

I'll go with QED, since it's newer and puts a magnifying glass on what Maxwell's equations are looking at.

 

[Dale]

Then it's a probability.

 

[nitsuj]

Then it's a probability.

So in QED a photon has a probable 4D position?

 

[Dale]

Essentially, yes. But I am not a QED expert.

 

[fluidistic]

As Whitham (1974) pointed out, many (if not most) waves are not governed by the "wave equation"!

(He gives a much broader definition, that a wave is "a recognizable signal that is transferred from one part of a medium to another with a recognizable velocity of propagation.")

Sounds interesting and quite surprising to me. Can you give one example please? And if we have "found" an equation that explain the wave, better.
Thanks.

 

[olivermsun]

Sounds interesting and quite surprising to me. Can you give one example please? And if we have "found" an equation that explain the wave, better.
Thanks.

Perhaps the most ubiquitous example would be surface water waves, which are governed by Laplace's equation,
\nabla^2\varphi = 0
where velocity is the gradient of the potential
\mathbf{u} = \nabla\varphi.

 

[Dale]

The resulting surface elevation is a solution to the wave equation. The fluid's velocity is not described by the wave equation, but the height of the ripples is. When people talk of water waves they are speaking about the ripples, not the velocity of the water molecules.

I don't think this is an example supporting your claim.

 

[olivermsun]

The resulting surface elevation is a solution to the wave equation. The fluid's velocity is not described by the wave equation, but the height of the ripples is. When people talk of water waves they are speaking about the ripples, not the velocity of the water molecules.

The motions of ripples in water are determined by the motions of the water, just as the motions of waves moving along a string are determined by the motions of the string itself.

The moving ripples in (deep) water are dispersive; solutions to the classical wave equation are not.

 

[Dale]

The motions of ripples in water are determined by the motions of the water

Certainly. But "determined by" is not "the same as".

The moving ripples in (deep) water are dispersive; solutions to the classical wave equation are not.

This is true. Dispersive waves are only approximately modeled by the classical wave equation. The approximation is bad for long times, but for short times it is reasonable. So I would still keep the definition and just indicate that dispersive waves are not ideal waves.

 

[olivermsun]

Dispersive waves are only approximately modeled by the classical wave equation. The approximation is bad for long times, but for short times it is reasonable. So I would still keep the definition and just indicate that dispersive waves are not ideal waves.

The behavior of dispersive water waves is fundamentally different from the hyperbolic waves that arise from the wave equation. You can see this easily and within a short time (relative to the wave period) from the way ripples crawl across the top of a wave 'bump' due to the difference between phase and group speeds.

I admit I do not really understand why one would want to define an entire class of interesting (and very well-studied) waves out of the discussion just because they don't fit an a "wave" equation which happens to arise from the physics of certain other kinds of ideal waves.

 

[Lavabug]

Perhaps the most ubiquitous example would be surface water waves, which are governed by Laplace's equation,
\nabla^2\varphi = 0
where velocity is the gradient of the potential
\mathbf{u} = \nabla\varphi.

Hope this doesn't make this thread too concrete, but I had to ask: the homogenous wave equation reduces to Laplace's equation if the perturbation on the surface of water doesn't depend explicitly on time yes? Also, your second statement (u being conservative), is this only valid for irrotational flows? Could surface water waves still be governed by Laplace's equation even if the velocity field was non-conservative? (I'm thinking of the sea sloshing around).

As for the OP: first start by looking at individual pulses. Think of tying a rope to a stake in the ground and giving it a jolt. You can think of a progressive wave as a sequence of jolts that move from point A to B. Ie: shock wave from a loud event, ripples on a pond etc. In these cases, the "jolt" is a rapid compression-decompression of air, or an elevation in water height, respectively, instead of a mountain formed on a rope by yanking it.

Consider fixing tying both ends of the rope or string to two stakes, then strumming the rope/string. This is essentially a musical instrument string. The waves are formed by two identical progressive waves that propagate in opposite directions along the string. Their sum produces what is called a standing or harmonic wave, which as its name implies doesn't go anywhere, as you've bounded both ends of the string.

You can extend this idea of standing waves to to 2-D by looking at how a drumskin vibrates, since its also "bounded" or " its ends are also fixed", so to speak.

I hope my wording is helpful.

 

[Dale]

I admit I do not really understand why one would want to define an entire class of interesting (and very well-studied) waves out of the discussion just because they don't fit an a "wave" equation which happens to arise from the physics of certain other kinds of ideal waves.

Mostly because I don't like any of the alternative definitions that I have seen. Like this one:

"a recognizable signal that is transferred from one part of a medium to another with a recognizable velocity of propagation."

IMO that is a poor scientific definition. What makes a signal and a propagation velocity "recognizable"? Does empty space count as a medium? Etc. If you pursue those rigorously you probably wind up with a wave equation anyway.

Just because something is approximately a wave doesn't mean that you cannot study or talk about it.

 

[EnergyHobo]

@Lavabug I believe you are correct with both statements. Laplace's equation only works for non-moving waves (time independent).

I believe the wave equation is something like:
\nabla^{2} \varphi = k\frac{\partial^{2}\varphi}{\partial^{2}t}

Then the derivative with respect to time would equal 0, which is Laplace's equation.

Also, rotational fields are non-conservative. I can't answer the second part of that question. Hope that helps.

 

[olivermsun]

Mostly because I don't like any of the alternative definitions that I have seen. Like this one:
"a recognizable signal that is transferred from one part of a medium to another with a recognizable velocity of propagation."
IMO that is a poor scientific definition. What makes a signal and a propagation velocity "recognizable"?

The problem is that many phenomena of interest escape a more precise definition. It's similar to asking "what is turbulence." The "poor scientific definition" that you so dislike is simply one of the working definitions offered by one of the more prominent mathematical physicists to study "waves" in general.

Does empty space count as a medium? Etc. If you pursue those rigorously you probably wind up with a wave equation anyway.

Just because something is approximately a wave doesn't mean that you cannot study or talk about it.

Except that you don't end up with a wave equation -- even approximately -- in the example of deep water waves or in many other examples which nevertheless seem to be full-blown "waves."

 

[olivermsun]

Hope this doesn't make this thread too concrete, but I had to ask: the homogenous wave equation reduces to Laplace's equation if the perturbation on the surface of water doesn't depend explicitly on time yes?

Laplace's equation only works for non-moving waves (time independent).

Water waves theory allows a surface perturbation which is explicitly time-dependent, so it is a somewhat different case.

Here you get Laplace's equation from the continuity equation rather than by assuming no time dependence.

Also, your second statement (u being conservative), is this only valid for irrotational flows? Could surface water waves still be governed by Laplace's equation even if the velocity field was non-conservative? (I'm thinking of the sea sloshing around).

The idealized water wave theory is built around inviscid flow around rest, no rotation, and so forth. This works fairly well since the Reynolds number is typically pretty big away from boundaries, the kind of waves we're talking about tend to be well above inertial frequency, etc.

Before I go too far off on a tangent, what kind of sloshing did you have in mind? Tidal or possibly seiches in the basins?

 

[Dale]

Except that you don't end up with a wave equation -- even approximately -- in the example of deep water waves or in many other examples which nevertheless seem to be full-blown "waves."

You have said that, but the examples so far are not very convincing. And in any case, they wouldn't qualify as waves according to the fuzzy definition either, except approximately.

 

[olivermsun]

Irrotational flow, Laplace's equation, surface boundary condition of balance between the potential and displacement*gravity ... do you find it unconvincing in a mathematical sense or a phenomenological one?

Do you agree that water waves are waves?

 

[Dale]

To a good approximation, yes. Although, I am not an expert on water waves.

I am unconvinced mathematically. As far as I know a monochromatic sinusoidal plane wave is a solution, so the problem can be formulated as a classical wave equation even if there exists an alternative formulation as Laplace's equation. Furthermore dispersive and nonlinear waves are still solutions to the classical wave equation where c is a function of wavelength or amplitude.

I see no reason to trade a clear definition for a sloppy one.

 

[Lavabug]

Water waves theory allows a surface perturbation which is explicitly time-dependent, so it is a somewhat different case.

Here you get Laplace's equation from the continuity equation rather than by assuming no time dependence.


The idealized water wave theory is built around inviscid flow around rest, no rotation, and so forth. This works fairly well since the Reynolds number is typically pretty big away from boundaries, the kind of waves we're talking about tend to be well above inertial frequency, etc.

Before I go too far off on a tangent, what kind of sloshing did you have in mind? Tidal or possibly seiches in the basins?

I see now. It also assumes incompressible flow since that's how the continuity equation reduces to Laplace's right?

Didn't have in mind the driving force behind the sloshing, just in general.

 

[olivermsun]

I am unconvinced mathematically. As far as I know a monochromatic sinusoidal plane wave is a solution, so the problem can be formulated as a classical wave equation even if there exists an alternative formulation as Laplace's equation. Furthermore dispersive and nonlinear waves are still solutions to the classical wave equation where c is a function of wavelength or amplitude.

Regarding dispersive effects, a nonlinear wave equation can be written for amplitude effects
c(u)^2 \nabla^2 u = \frac{\partial^2 u}{\partial t^2},
but how would you formulate this to include frequency-dependent dispersion? You could prescribe a phase speed for every Fourier component
c = \frac{\omega}{\kappa}
but how would you determine c as a function of x, t?

By contrast, the dispersion of deep water waves already captured by the linearized system which arises from the Laplace equation, and as a result you get the dispersion relationship right out of it. You don't need to introduce nonlinearity to describe this behavior.

It might be also be helpful to realize the "wave" propagates not just along the surface, but also through the body of water. That is, the stuff between the surface and the bottom matters (which is why the dispersion is depth-dependent).

In the limit of shallow water, the dispersive effects go away, and you do in fact recover the 2-d wave equation. So if you are to argue from this standpoint that all water waves are just shallow water waves (and hence obey the wave equation) with some corrections, then I suppose you could make a case for that. But they would not be small corrections in many cases..

I see no reason to trade a clear definition for a sloppy one.

I hope it's getting clearer rather than sloppier!

 

[Dale]

In the limit of shallow water, the dispersive effects go away, and you do in fact recover the 2-d wave equation. So if you are to argue from this standpoint that all water waves are just shallow water waves (and hence obey the wave equation) with some corrections, then I suppose you could make a case for that. But they would not be small corrections in many cases.

That is good enough for me.