Speed of a wave and its particles

[Celluhh]

i have a few questions which need clarification, so right now i will state my assumptions.


definition of the period of a wave : it is the timetaken for one point on the wave to complete one oscillation. and also the time taken to produce one complete wave.

definition of wave speed: in a time of one period, a crest on a wave will have moved a distance of one wavelength.

based on the definitions, i can deduce that the distance of one oscillation is the distance of one wavelength. which means that, if we freeze a wave at onepoint in time, and measure its wavelength, it will be of the same distance as that covered by a particle (thatmakes up the wave) after one oscillation. time taken to produce onecomplete wave is a period, tme taken for a crest on the wave to move a distance of one wavelength is also one period. since speed is distance over time, i can therefore deduce that fr the wave and the particles that make up the wave to cover the same distance over the same period of time, both their speeds must be the same. please correct me if i am wrong, however.

ps: i still don't get how a period is the time taken for one point on the wave to complete a distance of one wavelength and yet also the time taken for one wave to be completed. logically, this means that all particles that make up the wave will hve to start moving at th same time, which is impossible, as the wave would not even exist. but how then, can the particles complete one oscillation, and therefore one wave(many particles movin up and down at different times create a wave) (particles cover the same distance of one wavelength in one oscillation) in the same amount of time at the same speed if they don't actually start moving at the same time? but yet they can't.
no one has actually told me the answer i want yet, sadly...):


help will be greatly appreciated!;)

 

[phinds]

I'll leave it to the experts to get this right in details, but I think your fundamental flaw is a misunderstanding of the wave/particle duality. Light ACTS like a wave if you measure it in a way that sees waves and it ACTS like a particle (a SINGLE particle) if you measure it in a way that sees particles. It's NOT like there was a series of particles along the wave.

 

[BruceW]

Since this is in the general physics section, I'm going to assume Celluhh is not talking about light, but some classical wave such as waves on a string, or sound waves, or water waves, e.t.c.

Now we need to specify if we are talking about transverse or longitudinal waves. Since Celluhh mentioned crests, I am going to assume that means he/she wants to talk about transverse waves. And this is good because transverse waves are easier to imagine than longitudinal waves.

So after getting all that clear, I can say that this statement is wrong: "i can deduce that the distance of one oscillation is the distance of one wavelength" This is wrong because the oscillations are perpendicular to the direction of propagation (assuming transverse wave), so the distance of the oscillation has nothing to do with the wavelength. And if we talked about longitudinal waves, again the distance of oscillation is not related to the wavelength (but this is harder to imagine, since the oscillation and direction of propagation are the same).

 

[phinds]

Since this is in the general physics section, I'm going to assume Celluhh is not talking about light, but some classical wave such as waves on a string, or sound waves, or water waves, e.t.c.

seems like a bad assumption, since those waves don't HAVE "particles", they have "points", but you may be right.

 

[Infinitum]

based on the definitions, i can deduce that the distance of one oscillation is the distance of one wavelength. which means that, if we freeze a wave at onepoint in time, and measure its wavelength, it will be of the same distance as that covered by a particle (thatmakes up the wave) after one oscillation.

This is untrue. The distance covered by the particle has nothing to do with how far the wave has moved. To illustrate this, consider two waves in the attachment and suppose they have the same time period. The first one has the particles of the wave moving equal distance as the other since their amplitudes are equal, but the distance traveled by the waves are different.Edit : BruceW already beat me to the post

 

[Celluhh]

So y'all are saying that the distance of one oscillation of a particle that makes up the wave and the distance of one wavelength of the wave are two totally different things?

But then how come my textbook states that the period is time taken for a crest on the wave to Move a distance of one wavelength is the same as that taken by the crest to complete one oscillation? It doesn't make sense...

@phinds, brucew is correct. I am talking about transverse waves.

Thank you all for helping!

 

[nasu]

But then how come my textbook states that the period is time taken for a crest on the wave to Move a distance of one wavelength is the same as that taken by the crest to complete one oscillation? It doesn't make sense...

It sure makes sense as the two distances (wavelength and distance traveled during an oscillation) are "traveled" with different speeds.
The speed of the oscillation is not even constant but it has a harmonic time dependence (in the simplest case) and the maximum speed depends on the amplitude and frequency of the wave. Higher amplitude results in higher speed so the time taken for one complete oscillation is the same.
The speed of the propagation is independent of both amplitude and frequency (in linear, non-dispersive medium approximation).

 

[DragonPetter]

seems like a bad assumption, since those waves don't HAVE "particles", they have "points", but you may be right.

I think its a valid assumption based on the context. The particles are the matter of whatever medium the wave is propagating through, not the wave/particle duality of QM. In water, for example, the speed that these individual water particles move at plays a role in the speed of the propagating wave.

 

[jtbell]

But then how come my textbook states that the period is time taken for a crest on the wave to Move a distance of one wavelength is the same as that taken by the crest to complete one oscillation? It doesn't make sense...

@phinds, brucew is correct. I am talking about transverse waves.

Think of a cork bobbing up and down on the surface of water, as ripples pass underneath it. The crests of the ripples move horizontally, with a distance between them that we call the wavelength. The cork oscillates up and down, and we call the time for one complete oscillation the period.

Suppose we start a stopwatch when ripple (crest) #1 passes underneath the cork. One period later, ripple #1 has moved a distance of one wavelength away from the cork, ripple #2 is now underneath the cork, and the cork has completed one cycle of oscillation.

The individual water molecules basically move the same way the cork does, that is, up and down. They don't move horizontally along with the ripples.

 

[BruceW]

yeah, good explanation from jtbell :)

The molecules go up and down (or equivalently, the small section of string, or the small parcel of fluid), yet the crest moves to the side. So I often like to think of the moving crest as simply the illusion of a moving object. Because certainly there is no sideways movement of fluid, or string, or whatever.

It is natural to think that the fluid is moving along with the crest, but this is not true. So our intuition let's us down in this case (I remember I struggled with this when first learning it).

 

[jtbell]

So I often like to think of the moving crest as simply the illusion of a moving object.

Another example is a "wave" produced by people raising their arms in a football stadium. The "wave" travels horizontally, but the hands go up and down and the people stay where they are. (I don't know whether this example is meaningful outside the USA, though.)

However, this example is a different from the other waves because water waves, light waves etc. transport energy, but a "football-stadium wave" doesn't.

 

[DragonPetter]

Another example is a "wave" produced by people raising their arms in a football stadium. The "wave" travels horizontally, but the hands go up and down and the people stay where they are. (I don't know whether this example is meaningful outside the USA, though.)

However, this example is a different from the other waves because water waves, light waves etc. transport energy, but a "football-stadium wave" doesn't.

I'm not so sure that a football stadium "wave" does not transport energy. If you placed a party sized beach ball at one end of the football stadium wave, would it not travel to the other end if the conditions were right?

 

[Celluhh]

it's precisely because i understand perfectly how the particles making up a wave move up an down at different times to actually form a wave propagating to let's say, the mright, that i just cannot imagine how the particles all complete one oscillation in one period and at the same time one wavegets completed in that very same period. even if the distance of one oscillation and one wavelength is different,if the first particle starts its oscillation and transfers energy to the next particle to get it moving, and energy gets transferred from particle to particle until a wave is formed, the first particle will complete its oscillation way earlier than the other particles down thë wave, unless the last particle that gets the energy travels at about ten times faster a speed that the first particle and maybe five times faster a speed than the middle particles,will a wave be formed in one period. but logically, since the first particle starts off the wave, it also starts off the period, and hence only the firstparticle will be considered to have completed an oscillation in that period, whereas the other particles of the wave appear to have completed their oscillation in less than a period. do you get me?

i can understand why the wavelength and distance traveled in an oscillation are different, but only if the particles that makeup the wave travel at different speeds. i can also imagine why the speed of a wave and speed of particles that make up the wave are different though.

 

[BruceW]

hmm. Maybe start with imagining an arbitrary point on the wave. So this point will complete one oscillation in one period. And for a point next to that point it also completes one oscillation in one period. The only difference is that the phase is different.

So for example, one point might be at the top of its peak, and the next point might be just below the top of its peak, still on its way up. So from there, both points are doing oscillations with the same period, but the second one will always be a little bit behind the first one (in terms of its phase).

This is an explanation as if there were a discrete number of points. But it is simple to take the limit as the number of points goes to infinity, to get the behaviour shown by a continuous, ideal string.

 

[nasu]

even if the distance of one oscillation and one wavelength is different,if the first particle starts its oscillation and transfers energy to the next particle to get it moving, and energy gets transferred from particle to particle until a wave is formed, the first particle will complete its oscillation way earlier than the other particles down thë wave, unless the last particle that gets the energy travels at about ten times faster a speed that the first particle and maybe five times faster a speed than the middle particles,will a wave be formed in one period. but logically, since the first particle starts off the wave, it also starts off the period, and hence only the firstparticle will be considered to have completed an oscillation in that period, whereas the other particles of the wave appear to have completed their oscillation in less than a period. do you get me?

This description is OK and is difficult to see where your problem is.
Maybe in the word "completed" use earlier, in reference to a wavelength.
Considering a propagating wave, when the wave produced by particle A reaches a particles B situated one wavelength away, particle A has completed one period of oscillation whereas particle B is just starting to move. Particle B did not "complete" anything yet. But the wave traveled by one wavelength to reach B.

 

[Celluhh]

@brucew and nasu, yes of course. But nasu, tha particles of the wave that travels one wavelength to to b start their oscillations all at different times too . Unless you are saying that the period we are talking about starts at different times for each particle but is always of the same length?but then again as I said one complete wave can't be considered to have been formed in one period then.

 

[davenn]

...unless the last particle that gets the energy travels at about ten times faster a speed that the first particle and maybe five times faster a speed than the middle particles, will a wave be formed in one period.

if it was speeding up then the measurements of the speed of sound, for example, would be meaningless, as under your definition the speed would be contineously changing

D

 

[HallsofIvy]

@brucew and nasu, yes of course. But nasu, tha particles of the wave that travels one wavelength to to b start their oscillations all at different times too.

The whole point is that there is no particle of the wave that "travels one wave length". You can have a wave (in a wire, for example) that has a wavelength of 100 meters and an amplitude of 1 cm. While the wave "moves" one hundred yards along the wire, any particle of the wire moves up and down a total distance of 4 cm.

Unless you are saying that the period we are talking about starts at different times for each particle but is always of the same length?but then again as I said one complete wave can't be considered to have been formed in one period then.

Are you really clear on what a wave is?

 

[davenn]

ok some visualisations that maybe will help
these are from my interests in geology They show the direction of propagation of a way V's the particle motion within the material that the wave is passing through.

grrr ... discovered that they are too big kb size to post here
did a quick www page to show them

here's a link to my site that shows the wave animation graphics
seismic waves

Celluhh, take particular note of the particle motion

Dave

 

[nasu]

Unless you are saying that the period we are talking about starts at different times for each particle but is always of the same length?but then again as I said one complete wave can't be considered to have been formed in one period then.

"One complete wave" is misleading. It may be used as a short for one wavelength.
Other than that, it does not mean much. A wave (as a phenomenon) is not some sort of finite object so we can have fractions of it.
The wave is not "formed" in a specific time and exists afterwards. There is a perturbation somewhere in the medium and this perturbation propagates to other parts of the medium. This propagation is what is called a wave. There is no moment at which the wave is more "complete" than at other moments.

And yes, various points in the wave have different phases. This means that they all complete one oscillation in the same time but they are not doing the same thing at the same time. When one goes up another may go down and so on. Various particles will start oscillating at various times, the ones farther away from the source at later times. So you can say that they start their cycle at different times.

 

[Celluhh]

@nasu yes so as u said since thy start their cycle at different times, how can they complete the cycle at the same time?

 

[Celluhh]

But when we measure speed of sound we measure speed of the sound wave, not speed of the particles so it wouldn't affect right ?

 

[Celluhh]

@hallsofivy yep sorry my mistake I meant distance traveled by a particle

 

[davenn]

@nasu yes so as u said since thy start their cycle at different times, how can they complete the cycle at the same time?

they dont, what made you think that they do ?

did you look at the link and www page I did for you ?

Dave

 

[nasu]

@nasu yes so as u said since thy start their cycle at different times, how can they complete the cycle at the same time?

Are you confused about "Complete in the same time" versus "complete at the same time"?
They start at different times and finish at different times. The time for a cycle (the period) is what is the same.

 

[Celluhh]

@ nasu and dave, oh gosh both of you hit the nail on the head. so the particles don't complete their oscillation at the same time? ok, so a wavelength is created by particles all at different phases? but then when the first particle completes its oscillation and the last particle has perhaps just started,the last particle would transfer its energy to the next particle which would start moving too, with a little time lag, and it goes on and on. how then, do we know when a wave is complete?when the dipper goes into the water again? when the first particle starts its next oscillation?

so th speed of a particle is constantly changing, but the speed of all the particles at the same phase ( as in when one particle gos up then comes down when the next particle goes up)are the same, as they are supplied with the same amount of energy? they complete one oscillation in the same time but not at the same time, hence a wave is formed as a result. the source affects te frequency and period of the wave, but because of the constant regular movement of the source(eg. a dipper) the frequency and period of the waves created remain the same. am i right?

so I've learned that the distance of one particle oscillation and the distance of one wavelength of the wave created is different. ok i can visualise why.
y'all say the speed of the wave is different from the speed of the particles that make up the wave, i can understand why since the distance is different although the time is the same.

 

[davenn]

@ nasu and dave, oh gosh both of you hit the nail on the head. so the particles don't complete their oscillation at the same time? ok, so a wavelength is created by particles all at different phases? but then when the first particle completes its oscillation and the last particle has perhaps just started,the last particle would transfer its energy to the next particle which would start moving too, with a little time lag, and it goes on and on. how then, do we know when a wave is complete?when the dipper goes into the water again? when the first particle starts its next oscillation?

the wave has completed (ended) for a given particle when it is no longer oscillating... ie. it has returned to its rest state. ( if we are referring to water in a pond, as the ripples (waves) spread out from the point of origin, they pass by the "particles " of water and those particles rise up and down about their rest position -- the normal level surface of the water)

so th speed of a particle is constantly changing, but the speed of all the particles at the same phase ( as in when one particle gos up then comes down when the next particle goes up)are the same, as they are supplied with the same amount of energy? they complete one oscillation in the same time but not at the same time, hence a wave is formed as a result. the source affects te frequency and period of the wave, but because of the constant regular movement of the source(eg. a dipper) the frequency and period of the waves created remain the same. am i right?

No the speed of the particle is constant, else we could not say that the wave has a given frequency ... ie. "x" number of oscillations (cycles) per second.

so I've learned that the distance of one particle oscillation and the distance of one wavelength of the wave created is different. ok i can visualise why.
y'all say the speed of the wave is different from the speed of the particles that make up the wave, i can understand why since the distance is different although the time is the same.

great :)

cheers
Dave

 

[davenn]

OK one more little visualisation for you :)

look at the wave in this pic...

assume the horizontal line is the level surface of the pond water.
and the red dot is a cork sitting on the surface of the water

now in your mind move the wave in the direction shown, what is going to happen to the red
dot as the wave encounters it ? visualise how the red dot is first going to move down to the lowest part of the wave ( the bottom of the cycle) then come back up and through what was the flat surface level then its going to continue up to the wave peak and then start coming back down again. and continue doing that until there are no more waves passing by.

NOTE !
1) this is a traverse wave, the particle motion is perpendicular to the direction of travel of the wave
2) that the red dot doesn't move foreward along with the wave. it ONLY "bobs" up and down as the wave passes by

cheers
Dave

 

[Celluhh]

the wave has completed (ended) for a given particle when it is no longer oscillating... ie. it has returned to its rest state.

um I don't get you ... ( if we are referring to water in a pond, as the ripples (waves) spread out from the point of origin, they pass by the "particles " of water and those particles rise up and down about their rest position -- the normal level surface of the water)



No the speed of the particle is constant, else we could not say that the wave has a given frequency ... ie. "x" number of oscillations (cycles) per second.

But someone said it has different velocity at different phases of its oscillation...

 

[Celluhh]

Ok so I need to check my understanding. Firstly, a wave gets completed in one period. An oscillation by a particle also gets completed in one period. As the first particle starts its oscillation, it passes on its energy to another particle and continues with its oscillation. Then, the second particle starts its oscillation and passes on its energy to the third particle, and also continuues with its oscillation. So, this continues on with all the particle till a visible transverse wave is formed. The first particle, once done with its oscillatioitself in its rest position. The last particle may hve just started its oscillation but we count all the particles, including first all the way to the second last, which are all in different phases of their oscillations, as one complete transverse wave/ one wavelength. Am I correct?


I didnt count the last particle as the last particle must be in the same phase as the first particle because wavelength is distance between two particles in phase...am I correct?? And although the particles have not all completed their oscillations except for the first particle, they being in different phases forms a complete wave after one period( which is the time taken by the first particle to complete its oscillation) am I right??

 

[BruceW]

But someone said it has different velocity at different phases of its oscillation...

The particles (or fluid elements) will have different velocity at different parts of their oscillation, but this is the velocity of a certain molecule. The velocity of the wave is a different thing!

 

[BruceW]

Ok so I need to check my understanding. Firstly, a wave gets completed in one period. An oscillation by a particle also gets completed in one period. As the first particle starts its oscillation, it passes on its energy to another particle and continues with its oscillation. Then, the second particle starts its oscillation and passes on its energy to the third particle, and also continuues with its oscillation. So, this continues on with all the particle till a visible transverse wave is formed. The first particle, once done with its oscillatioitself in its rest position.

If you want to start thinking about how a wave is formed, it gets a bit more complicated, because the wave is made up of a superposition of different frequencies. (And therefore there is not just a single defined period).

But if you think about a wave that is made up of one frequency, then you can say that there is just a single, defined period. But then in this case, the wave has no origin to speak of. This is the simplest kind of wave, so this is the one you should get to grips with first.

 

[Celluhh]

Yup, so can you help me ?

 

[BruceW]

What specifically did you want help on? Your understanding of single-frequency waves seems pretty good to me. If you can find some practice questions, it would probably be useful to try them, because that is one of the best ways to find out whether you really do understand it. Or, alternatively, to try to explain a topic to someone, because that tests your knowledge of the topic pretty well.

 

[Celluhh]

I just can't seem to visualise how a complete wave gets formed in exactly
One period ... How is it that all wavelengths get formed in exactly one
Period...

 

[sophiecentaur]

?
The definition of a period is the length of time it takes for that to happen. The 'exactness' is from the definition.
What else could happen? If you find it difficult to answer that question then that could suggest an answer to your question.

 

[BruceW]

I'm not sure what is meant by "gets formed" ? Is that supposed to mean something about how the system goes from 'no wave' to 'wave' ?

Or does it mean in the case when the wave is always there, and how each particle goes through its oscillation?

 

[sophiecentaur]

I just can't seem to visualise how a complete wave gets formed in exactly
One period ... How is it that all wavelengths get formed in exactly one
Period...

I just re-read your post No26. You seemed to have got things well sorted out in that post. I don't see why you as the above question except that you may not have grasped the following point. When one particle is moving, it is the result of the 'previous particle' moving and its motion lags slightly behind the previous particle. This is because of its mass and the spring constant (or equivalent) associated with the forces that couple them together. Similarly, the 'next particle' will move, but slightly lagging with respect to the middle particles. Every particle will move in the same way but just in a different phase. The lower the masses and the stiffer the coupling, the less lag there will be - so the quicker the forces will be transmitted and the longer the wavelength will be. For massive particles and soggy springs, the disturbance will take longer to travel - so the wavelength will be shorter.
This follows the wave equation c=λf. Once you have established the value of c, f and λ are bound together. (f being 1/the period of oscillation)

 

[xAxis]

I think I know what is the problem. You don't understand why while the first particle, tho source, makes one oscilation, the wave has traveled exactly one wavewlent "down the line". I.e. why not half wavelents, or 1.23 wavelents or any other number.
Is that what you can't visualise?

 

[Celluhh]

I think I know what is the problem. You don't understand why while the first particle, tho source, makes one oscilation, the wave has traveled exactly one wavewlent "down the line". I.e. why not half wavelents, or 1.23 wavelents or any other number.
Is that what you can't visualise?

yep,bingo.

 

[BruceW]

mathematically speaking, it is because we have specified that the wave has only one frequency. And as sophiecentaur said, this means the wavelength is then fixed.

 

[sophiecentaur]

yep,bingo.

If you are having this problem then I think it's because you are putting the cart before the horse.
The fact is that there must be a delay in the propagation of the disturbance down the line. For a uniform system, after a while, the situation will establish a steady state, with waves traveling from the loudspeaker / driver / whatever. The distance that a particular amount of displaacement (say a maximum) happens to get from the source before the source is again at a maximum, is called the length of the wave. This only applies to a repeated wave - usually a sine wave - of course. If you send a single pulse down the line then there is not an identifiable 'wavelength'. If you think in terms of a propagation delay causing a physical spacing of points along the wave then wave'length' follows. Start with speed and frequency and the idea of a λ then comes out of it.

 

[xAxis]

Well, consider the simplest form of wave where exactly one particle is excited to vibrate, end let it be the first one on the left in some elastic strip . Now think that wave is transfer of energy, so as the first particle goes up from equilibrium position, the next one to the right follows, but it follows in exactly the same manner. But now think what happenes to the 3rd particle. It follows exactly the same motion of the 2.nd particle. So does the 4.th particle and so on. (we are assuming only one particle streight line as a medium) So you can see how as particle goes up, the wave travels to the right. But don't forget that that right movement of the wave is nothing but the transfer of energy, which is the transfer of motion of the first particle.This happens almost instantly between two particles, but there is a small lag. So the next particle will always be little behind the previous, but it's motion (oscilation) will be identical.
Now imagine the moment when the first particle's just finished the first oscillation. Because the lag in transfering energy is so small, the second particle has almost finnished it's first oscillation and so on. Looking in the direction of the wave propagation, you will see "backward chronological copy" of the movement of the first particle, because all the particles' motions are exact copies of the motion of the preceding particle.

 

[Celluhh]

@xaxis, and so your point is ?

 

[Celluhh]

The distance that a particular amount of displaacement (say a maximum) happens to get from the source before the source is again at a maximum, is called the length of the wave. This only applies to a repeated wave - usually a sine wave - of course. it.

I don't understand what you mean...

 

[sophiecentaur]

If you take a rope and just give it a jerk then there is just an impulse passing along it. There is no 'wavelength'. If you set up a continuous side to side motion then a continuous progressive wave is set up. Each piece of the rope will oscillate continuously. The distance between two pieces is a wavelength (or a whole number of wavelengths) when their motions are in step. We are discussing continuous waves, aren't we?

 

[xAxis]

@xaxis, and so your point is ?

I tried to help you visualise. So just imagine the picture I propose. there is a streep which is say one molecule thin, like a line of molecules.
Now imagine the moment when the first particle's just finished the first oscillation. Because the lag in transfering energy is so small, the second particle has almost finnished it's first oscillation. So if you can see that (together with "backwards time copy") the wave started traveling to the right almost the same instant that the first particle started first oscilation, it shouldn't be difficult to see that now, as it have finished, the wave has traveled down the line some distance. But remember the main point of wave? The motion of it is because the motion of the source (up down oscillation) is comunicated to the next particle. Now you should be able to see that that distance cannot be more than one wavelent because it would mean that some particles have already finnished one full osculation and started the second, but it cannot be cause their motion is just the copy of the motion of previous particle, and none of them had finnished full oscilation. Does this help?

 

[Celluhh]

@xaxis yup ok so for this to happen all particles are traveling at the same speed right ?

 

[sophiecentaur]

If you look at the Maths, it is described perfectly for sinusoidal wave:
d = A sin(ωt - 2πx/λ)
where d is the displacement at time t and distance x, ω is the angular frequency and λ is the wavelength.
A particle at distance x is vibrating at the rate ω/2π times per second and the phase of its vibration lags by x/λ.
'Why' the wave repeats itself every λ is not an answerable question. The fact is that it does repeat itself (it has to return to a mean position every cycle and the pattern will be regular) and the distances involved must be regular. The wavelength is DEFINED by this spacing and the spacing is determined by the stiffness and density (or some equivalent pair of quantities) of the medium that carries the waves.
How do the particles "know" where to be at any time? They don't; it just takes time for the forces to propagate through the medium and to move them into the appropriate places at the appropriate speeds.

 

[xAxis]

@xaxis yup ok so for this to happen all particles are traveling at the same speed right ?

Particles don't travell in the direction of the wave. Their speed is zero (so yes, they're all traveling at the same speed :) ).
Oscilating particle has only vertical speed (in this ideal case). That speed changes according to v(t) = awsin(wt). This speed is maximal when particle is in equilibrium position. So that the first particle starts oscillation up for instance with its maximum speed. It decelerates and reaches zero at maximum distance 'a' which we call amplitud of the wave. But this motion is vertical. Particles never travel along the wave. It only comunicate it's motion to the next particle and this takes some time. And this comunication is the actual 'speed of wave'. All the particles in the medium are motionless in the wave direction.