Why do waves move in a direction?

[Unified28]

One thing which puzzles me is why do waves move in a direction? A spring oscillates up and down, but a wave oscillates and moves forwards. Why does it move in the forwards direction and not randomly backwards? Thanks for any answers!

 

[Nemoto]

I am much less knowledgeable than many on this site, so if I have got anything about my answer wrong, I hope someone else will correct it. Here is my take on it:

If a pebble is dropped into a pond, waves will propagate outwards due to the displacement of the water at the point of impact. However, once the waves reach the edge of the pond, they can not move any further outwards. If their kinetic energy is not all spent, they will rebound, interfering with the outward bound waves. If the body of water is too large for this to occur, only outward waves will be seen. This may seem similar to a spring, but it is dependent on the propagation of waves outwards from an original point.

In the case of light, a laser is required to send all the waves in one direction. The double split experiment shows ordinary light waves propagating outwards from the point of emission in much the same way as waves in a pond. This is why a wide interference pattern is produced.

The situation with a spring is different in that it has to do with the material composition of the spring. A plastic "Slinky" toy may appear similar to a spring but its behaviour is different as it cannot bounce. A spring made of spring steel may be compressed, storing kinetic energy, which is then utilized as the spring is released, causing the oscillating, or bouncing, behaviour. The kinetic energy is held within the material of the spring, not in the medium surrounding it.

Nevertheless, if a "boing" sound is heard, then waves are propagating outwards from the point of impact of the spring with a surface, through the medium of the surrounding air. This oscillating air has struck your eardrum, allowing you to hear the sound. It was not a directional wave, however, any more than the wave in the pond or the light wave. This can easily be demonstrated by having a few other people around the room hear the same "boing".

 

[blue_leaf77]

Why does it move in the forwards direction and not randomly backwards?

When you wrote this, were you imagining certain physical phenomenon in mind? It's still not very clear to me what you mean by "randomly backwards".
Just for an information which probably pertains what you may have assumed, there is spherical wave in which the disturbance propagates isotropically in all directions. What is required for a disturbance to be called a wave is that it satisfies the wave equation.

 

[Unified28]

I am much less knowledgeable than many on this site, so if I have got anything about my answer wrong, I hope someone else will correct it. Here is my take on it:

If a pebble is dropped into a pond, waves will propagate outwards due to the displacement of the water at the point of impact. However, once the waves reach the edge of the pond, they can not move any further outwards. If their kinetic energy is not all spent, they will rebound, interfering with the outward bound waves. If the body of water is too large for this to occur, only outward waves will be seen. This may seem similar to a spring, but it is dependent on the propagation of waves outwards from an original point.

In the case of light, a laser is required to send all the waves in one direction. The double split experiment shows ordinary light waves propagating outwards from the point of emission in much the same way as waves in a pond. This is why a wide interference pattern is produced.

The situation with a spring is different in that it has to do with the material composition of the spring. A plastic "Slinky" toy may appear similar to a spring but its behaviour is different as it cannot bounce. A spring made of spring steel may be compressed, storing kinetic energy, which is then utilized as the spring is released, causing the oscillating, or bouncing, behaviour. The kinetic energy is held within the material of the spring, not in the medium surrounding it.

Nevertheless, if a "boing" sound is heard, then waves are propagating outwards from the point of impact of the spring with a surface, through the medium of the surrounding air. This oscillating air has struck your eardrum, allowing you to hear the sound. It was not a directional wave, however, any more than the wave in the pond or the light wave. This can easily be demonstrated by having a few other people around the room hear the same "boing".

I think you are absolutely right, and yes it might be interesting to know that the cause is due to the initial forward force. Yet I am trying to understand it in more fundamental terms. It seems as if it is some strange property of space that an up and down motion in one dimension causes movement in the perpendicular dimension. How do the dimensions relate to explain this?

When you wrote this, were you imagining certain physical phenomenon in mind? It's still not very clear to me what you mean by "randomly backwards".
Just for an information which probably pertains what you may have assumed, there is spherical wave in which the disturbance propagates isotropically in all directions. What is required for a disturbance to be called a wave is that it satisfies the wave equation.

A wave is oscillating up and down, and then it moves in the perpendicular direction. How fast it propagates seems to depend on the tension of the wave according to experiments. I am wondering how does the oscillating movement relate to the perpendicular movement of the wave? It moves up and down, yet it has a relation to the forward motion of the wave due to that the wave speed depends on the tension within the wave. However how can an up and down motion determine the direction of the perpendicular motion? As in why doesn't it oscilalte up then down and then backwards? Why forwards? I would consider a spherical wave as a sum of many smaller waves traveling in one direction.

 

[blue_leaf77]

In the wave propagation along a string, the propagating disturbance is caused by the presence of tension that acts along the string.

As in why doesn't it oscilalte up then down and then backwards?

The backward propagation as well as the forward one form a pair of solution to the wave equation. What you perhaps refer to in this case is probably a string held at one end and give a pounding. Imagine now you pick one section around the middle of the string while letting both ends loose, give a pounding and you will observe two crests propagating towards the two ends.

 

[Unified28]

In the wave propagation along a string, the propagating disturbance is caused by the presence of tension that acts along the string.

The backward propagation as well as the forward one form a pair of solution to the wave equation. What you perhaps refer to in this case is probably a string held at one end and give a pounding. Imagine now you pick one section around the middle of the string while letting both ends loose, give a pounding and you will observe two crests propagating towards the two ends.

Yes maybe I got it now thanks to your replies. So since it's along the string, and the string was initially pushed, whatever force pulls the wave up or down is due to a diagonal vector implying a force in the forward direction.

 

[Nemoto]

I think you are absolutely right, and yes it might be interesting to know that the cause is due to the initial forward force. Yet I am trying to understand it in more fundamental terms. It seems as if it is some strange property of space that an up and down motion in one dimension causes movement in the perpendicular dimension. How do the dimensions relate to explain this?
A wave is oscillating up and down, and then it moves in the perpendicular direction. How fast it propagates seems to depend on the tension of the wave according to experiments. I am wondering how does the oscillating movement relate to the perpendicular movement of the wave? It moves up and down, yet it has a relation to the forward motion of the wave due to that the wave speed depends on the tension within the wave. However how can an up and down motion determine the direction of the perpendicular motion? As in why doesn't it oscillate up then down and then backwards? Why forwards? I would consider a spherical wave as a sum of many smaller waves traveling in one direction.

I am sorry, but I do not quite understand this. What sort of wave oscillates up and down and why? Why does it then move in a perpendicular direction?
Waves propagate at different speeds through different media due to the absorption of energy. This is why waves caused by a dropped pebble eventually die out. The pebble falls in the water and it hits some molecules of water. These vibrate and hit the ones next to them, and so on, but each time a little of the energy is absorbed as electrons within the atoms also vibrate. Can you show where you got the idea of tension from? As for up and down motion causing motion in a direction perpendicular to it, try jumping up and down on an upstairs floor in an old house, and you can experience this for yourself. A drum skin does the same thing when it is struck. The waves are spreading outwards from the point of impact, just as with water. A drum skin or a floor are acting in two dimensions though. Air or water would allow a wave to propagate outwards in three dimensions by the same mechanism, thereby being spherical. The waves are spreading outwards and growing from the centre, not traveling in one direction.

 

[Unified28]

I am sorry, but I do not quite understand this. What sort of wave oscillates up and down and why? Why does it then move in a perpendicular direction?
Waves propagate at different speeds through different media due to the absorption of energy. This is why waves caused by a dropped pebble eventually die out. The pebble falls in the water and it hits some molecules of water. These vibrate and hit the ones next to them, and so on, but each time a little of the energy is absorbed as electrons within the atoms also vibrate. Can you show where you got the idea of tension from? As for up and down motion causing motion in a direction perpendicular to it, try jumping up and down on an upstairs floor in an old house, and you can experience this for yourself. A drum skin does the same thing when it is struck. The waves are spreading outwards from the point of impact, just as with water. A drum skin or a floor are acting in two dimensions though. Air or water would allow a wave to propagate outwards in three dimensions by the same mechanism, thereby being spherical. The waves are spreading outwards and growing from the centre, not traveling in one direction.

Here is an example of how oscillations and waves are related to each other. Check the simple harmonic motion chapter: http://agni.phys.iit.edu/~vpa/wavesosci.html

This is where I got the idea of tension, I googled it sometime ago. http://www.physicsclassroom.com/class/waves/Lesson-2/The-Speed-of-a-Wave

I was curious about how oscillations and wave speed relate to each other while being in perpendicular dimensions. But I suppose that whatever force is accelerating the oscillation must be a diagonal vector. That is at least my guess for now.

Yes it is a spherical wave, but who said that it is "one" wave such that the defined "oneness" has a relevance to reality? It is certainly too macroscopic to be one quantum state. Thus it is a collection of smaller parts, molecules in this case, moving in different directions due to different forces.

 

[blue_leaf77]

The waves are spreading outwards and growing from the centre, not traveling in one direction.

One should also pay attention to the available degree of freedom of the system. In a wave propagation in a string, there is effectively one degree of freedom in space. And when one of the ends is held as well as connected to the disturbance generator, then obviously the wave can only be propagating forward. Backward propagation is impossible simply and trivially because there is no part of the string beyond its end.

 

[Nemoto]

Here is an example of how oscillations and waves are related to each other. Check the simple harmonic motion chapter: http://agni.phys.iit.edu/~vpa/wavesosci.html

This is where I got the idea of tension, I googled it sometime ago. http://www.physicsclassroom.com/class/waves/Lesson-2/The-Speed-of-a-Wave

I was curious about how oscillations and wave speed relate to each other while being in perpendicular dimensions. But I suppose that whatever force is accelerating the oscillation must be a diagonal vector. That is at least my guess for now.

Yes it is a spherical wave, but who said that it is "one" wave such that the defined "oneness" has a relevance to reality? It is certainly too macroscopic to be one quantum state. Thus it is a collection of smaller parts, molecules in this case, moving in different directions due to different forces.

Looking at the first site you have cited, I see that the page is secondary to one on acceleration with alternating electric and magnetic fields. It is true that electric and magnetic fields are perpendicular to each other. After this are discussed oscillations and properties of periodic harmonic motion, mass on a spring and a simple pendulum. I do not fully trust this site however, as it has spelling mistakes, and what appear to be pages scanned in from a textbook, which suggest that it is not very professional.
The other site is discussing waves in the ocean, in the air, as with an echo, and in a rope. Tension applies to the speed of the wave in a string or rope, because the rope is the medium through which the wave is propagating.
As for the oneness or otherwise of a wave, this is a bit too philosophical for me.

 

[SteamKing]

I am sorry, but I do not quite understand this. What sort of wave oscillates up and down and why? Why does it then move in a perpendicular direction?

There are two kinds of wave: longitudinal and transverse.

The longitudinal wave oscillates in the direction of travel; the transverse wave oscillates perpendicular to the direction of travel.

Sound waves are examples of longitudinal waves.

Water waves are examples of transverse waves.

http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

 

[crador]

I think we have veered off target here guys. Is the question not: why does the wave continue in one direction, instead of randomly turning around?

Equivalently: If you have a 1D wave propagating (on a string or what have you), and you freeze time/ take a picture of it, how can you predict/tell from that snapshot which direction it will move in the next moment?

Answer: You can't, you need information about the velocity along the string as well to tell which direction it is going. In terms of water waves the front is rising, and the back is falling.

Did that help?

 

[blue_leaf77]

why does the wave continue in one direction, instead of randomly turning around?

The solutions of wave equation are called modes, in our problem the forward and backward propagation of wave on a string are the two distinct modes. Modes can be regarded as the set of basis in the solution space of the wave equation, which is to say that any linear combination of those modes also satisfies the wave equation the individual mode satisfy. The nature of a basis function is that they are independent, the contribution/presence of one mode cannot be influenced by another different one. Therefore the forward propagating wave on a string cannot randomly give rise to the backward one, because they are different mode.

 

[Nemoto]

There are two kinds of wave: longitudinal and transverse.

The longitudinal wave oscillates in the direction of travel; the transverse wave oscillates perpendicular to the direction of travel.

Sound waves are examples of longitudinal waves.

Water waves are examples of transverse waves.

http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

Thank you, this link is most interesting. I love the animations as they really help me to understand better.

 

[Unified28]

Looking at the first site you have cited, I see that the page is secondary to one on acceleration with alternating electric and magnetic fields. It is true that electric and magnetic fields are perpendicular to each other. After this are discussed oscillations and properties of periodic harmonic motion, mass on a spring and a simple pendulum. I do not fully trust this site however, as it has spelling mistakes, and what appear to be pages scanned in from a textbook, which suggest that it is not very professional.
The other site is discussing waves in the ocean, in the air, as with an echo, and in a rope. Tension applies to the speed of the wave in a string or rope, because the rope is the medium through which the wave is propagating.
As for the oneness or otherwise of a wave, this is a bit too philosophical for me.

Even if a site isn't professional I have always thought that it is overrated that they have to be trustable etc. I remember that I was shocked when my teacher told me that I couldn't link to wikipedia when writing my thesis. I will try to describe the relationship between waves and oscillations. A wave has the property that the matter itself does not move while the energy does. Each individual particle within the wave oscillates up and down like a spring. The molecular bindings between molecules forces the other molecules to also follow in its oscillation. However if the molecules are slightly pushed the back of the wave will push the molecules not only up and down but forwards as well. I suppose that is how it works.

In any medium there is tension between particles. I believe that it is the fundamental cause behind wave motion and the explanation for oscillations such as how force increases with distance from equilibrium.

When you said that "a" wave can be spherical, you referred to it as one wave moving in different directions at once. In terms of language that is a correct statement. Fundamentally in physics these wave motions are constituted by separate vibrations each propagating in different directions.

 

[crador]

The solutions of wave equation are called modes, in our problem the forward and backward propagation of wave on a string are the two distinct modes. Modes can be regarded as the set of basis in the solution space of the wave equation, which is to say that any linear combination of those modes also satisfies the wave equation the individual mode satisfy. The nature of a basis function is that they are independent, the contribution/presence of one mode cannot be influenced by another different one. Therefore the forward propagating wave on a string cannot randomly give rise to the backward one, because they are different mode.

That is all well and great as a mathematician, but doesn't tell us much as physicists. Moreover, as a mathematician you have avoided the question.

Let me reformulate the question and answer in terms of math for you:

Given u(x,0) where u(x,t) is the solution to the problem at hand (wave on unbounded interval), how can we determine u(x,t)? Answer: insufficient information, also need u'(x,0) to solve wave equation.

Physics:

How can we tell a forward moving wave from a backward one/ why doesn't it turn around? Ans: by looking at the velocity distribution -- front of the wave going up, back going down.

Basis/superposition is irrelevant for this basic question -- would help more for problems like the drumhead or hydrogen atom.

 

[blue_leaf77]

How can we tell a forward moving wave from a backward one

By just taking a photograph at an instant of time and not knowing its initial condition, you can't.

why doesn't it turn around?

When there is no change in the system, why should it turn around. Nature always prefers to maintain its previous condition due to the law of inertia.

front of the wave going up, back going down.

Not necessarily, it depends on how it was triggered at the starting point. If the string was plucked downward, then the front will be the trough.

 

[crador]

OP: you have the answer you were seeking, hopefully.

I think the fact that we are beginning to cite previous posts selectively while ignoring the conclusions in the same posts means it is time for me to go, and the thread to be closed.

 

[rumborak]

What I'm somewhat missing in this thread, and what I think might elucidate the matter further, is Huygen's Principle. So, each point can be considered a point source, and should be actually. A given point in space/water doesn't know whether the wave is traveling left or right. It only pulls on its neighbors.
So, even though you see a wave front travel from left to right, there *is* in fact a back-traveling part, but it sort of cancels itself out.

 

[crador]

What I'm somewhat missing in this thread, and what I think might elucidate the matter further, is Huygen's Principle. So, each point can be considered a point source, and should be actually. A given point in space/water doesn't know whether the wave is traveling left or right. It only pulls on its neighbors.
So, even though you see a wave front travel from left to right, there *is* in fact a back-traveling part, but it sort of cancels itself out.

No, the Huygens-Fresnel's principle says that each point can be considered a point source, but the resulting propagation is only in the "forwards" direction. Their principle doesn't explain why. It does say that there *is* NOT a backwards propagation. http://en.m.wikipedia.org/wiki/Huygens–Fresnel_principle

Excuse me for citing wikipedia.

The reason it is not backwards is due to inertia. The front of the wave is going one way, the back the other way (insert up/down or left/right -- whatever the case may be). That is to say, to get the real solution you also need to get the velocity distribution of the wave at the same point of time that you have the elevation distribution.

Or more simply:

Given u(x,0) where u(x,t) is the solution to the problem at hand (wave on unbounded interval), how can we determine u(x,t)? Answer: insufficient information, also need u'(x,0) to solve wave equation.

 

[crador]

Honestly guys, it should be very clear that all we need to know in classical mechanics is position, velocity, and acceleration in order to predict the system's future.

We have position, we lack velocity.

Acceleration is calculated from position and velocity according to the wave equation (speed of propagation tells us the tension due to deflections from the mean).

 

[rumborak]

Crador,

you are misunderstanding Huygen's principle. The point sources in Huygen's theory know of no direction; just like the wave equation says, all those point sources do is to indiscriminately excite their neighbors, in *all* directions.
The movement of the wave is actually an aggregate behavior of those point sources together. The phases between them constructively interfere in the forward direction, and destructively in the backward direction, resulting in the observable forward motion of the wave.

 

[crador]

Crador,

you are misunderstanding Huygen's principle. The point sources in Huygen's theory know of no direction; just like the wave equation says, all those point sources do is to indiscriminately excite their neighbors, in *all* directions.
The movement of the wave is actually an aggregate behavior of those point sources together. The phases between them constructively interfere in the forward direction, and destructively in the backward direction, resulting in the observable forward motion of the wave.

I fear I'll never understand this argument. The point sources know of no direction, and yet they conspire to interfere constructively in the forward direction, and destructively in the backward direction. By symmetry they should simply interfere constructively in both directions, and this is the solution you get when naively applying the wave equation to said point sources, while implicitly assuming that the initial velocity distribution is identically zero -- the error in the principle.

If you assume the velocity distribution is consistent with a forward moving wave (not zero everywhere), then the wave equation yields what we want: a foward traveling wave, with nothing traveling backwards.

Please accept that future events are not determined by only by instantaneous displacements, but also by inertial moments.

 

[rumborak]

I think in terms of intuitive understanding of the matter, it's no different than Fourier analysis. In the end, there you too have to accept that an infinite number of sine waves of infinite extent can come together to form a compact signal of finite extent.
And even in a much simpler example, two sine waves of the same but opposite frequency will already produce a standing wave that behaves very differently than its two constituent waves.

 

[crador]

In my experience with Fourier series you need a sufficient set of initial and boundary conditions in order to determine the coefficients and eigenvalues of each pair of sine/cosines (the eigenfunctions to the eigenvalues of the wave operator). Considering we have no boundary, the natural candidates for these requirements are u and u', i.e. the displacement and velocity.

So yes, an infinite number of sines and cosines come together to form the solution. Do you know how to choose what porportion each should have to the others? I do, and I just told you how, without having to say something like 'well these cancel by this rule of thumb, and these construct also because I say so'.

Here is where I have drawn my notions from, and it is a rather good introduction to the material at hand: ISBN 978-0470054567.

Maybe I'm missing something critical. I doubt it though, since I learned Huygen's principle in high school with the caveat of 'this is basically wrong, but an easy way to look at it', and then went on to learn how to solve PDE's in college.
Again, the argument of constructive interference in front, and destructive interference behind is incorrect by a simple symmetry argument. If I simply look from the other direction, then we expect the waves to constructively interfere backwards, and destructively forwards -- but no! we see by Huygen's principle that they move only forward, so I have changed the dynamics (direction of wave travel) of the system by observing it from the opposite direction.

Please leave a reference something I can read up on if you still think I am wrong, otherwise this is it for me!