What are the properties of transverse waves?

[Celluhh]

Ok, so the wavelength is the length between two crests. Is it also the length of a complete wave? (sorry if I sound really stupid) The period is the time taken for one particle that makes up the wave to complete its oscillation, and it is also the time taken to make one complete wave. But I don't understand why this is so. I may be complicating matters, but I can't seem to stop thinking about it until I get it right. There is energy being transferred from particle to particle in a wave. When the first particle gets its kinetic energy from the source of vibration, it starts to move up and down, and transfers its energy to anther particle or it to start moving up and down, and this continues for all consecutive particles which make up the eventual wave. Since there is time lost while energy is being transferred from one particle to
Another, doesn't this
Mean that the first particle will complete it's oscillation before the other particles. How then, will they all manage to make one complete wave in a particular period?

Here is the question that got me thinking:(it's not supposed to be tough, but again , I like to think a lot. )
The speed of a transverse wave on a string is 450m/s. while the wavelength is 0.18m. The amplitude of the wave is 2.0mm. How much time is required for a particle for the string to move through a total distance of 1.0 km? I can deduce from this that a particle on the string covers 8.0mm in one oscillation, but I don't see how how the wavelength applies when we are talking about the particles. If anyone can enlighten me on these questions whih have been bugging me since a few days ago, pls help . Thank you !

 

[lntz]

you are over complicating matters. the wave length is the distance between two crests or troughs in the wave, you are correct. but to think of a wave as some kind of 'dominoes' effect, is confusing. as long as the wave length remains constant, so will your time period. and if you want to consider all the particles moving in a wave, then yes, each particle is in a slightly different position within the wave, but this does not mean that they have a slower time period.

 

[Celluhh]

But how can all the particles in a wave gain kinetic energy at the same time, if that is so it won't be a wave anymore... Ok maybe I don't make sense.

 

[lntz]

consider a single photon traveling in a straight line. it has energy, and it is oscillating through a wave form.

the particles in the string don't get given the energy all at the same instant, which is why parts of the string are in different parts of the wave. a wave travels through a medium, like you said, by passing on it's energy.

when i say 'time period' i am referring to the time it takes for the particle to move through 2pi radians, not the time at which that particle was given energy.

if you drop two identical balls onto a surface, at different times, they won't hit the ground at the same time, nor will they reach their highest point at the same time, but the time it takes for them both to do this, will be the same.

 

[Celluhh]

Exactly! Because the time period is the same, the dirt particle will finish its oscillation faster than others, won't it ??

 

[lntz]

yes. so the wave moves on through the medium.

 

[Celluhh]

Yeah so how can one complete wave be made by the respective particles in the same time period??

 

[lntz]

because if i start counting to ten at t=0 and you start counting to ten at t=1, i will reach ten before you do, but it will still take us both ten seconds to complete the count.

this would be easier if i could draw some diagrams for you.

 

[Celluhh]

If we are supposed to add up to twenty, at the end of ten seconds, we would only be nineteen!

 

[lntz]

you misunderstand. if i am saying the time period of a certain event is ten seconds, it takes ten seconds for that event to complete.

it makes no difference when another event starts, yours takes ten seconds too.

your event doesn't stop simply because i finish before you.

i think it would be useful for you to find some short and clearly defined definitions of wavelength, frequency, and time period.

 

[Celluhh]

The period is the time taken to complete one wave. But at the end of the period, due to all the particles needing the same time to complete one oscillation, which is something like both of us needing 10s to complete the race, there is no way a complete wave would be formed once the period is up, and some particles re still halfway into their oscillation.

Can I ask u something to see if we are actually visualising the same thing?? To you, when a particle on the wave comPletes one oscillation, does that mean a complete wave cycle is formed?

 

[lntz]

yes, the particle starts at 0 radians, it then moves to pi/2 radians and so on, completing a whole 2pi radian rotation.

2pi radians = 360 degrees.

there are 2 pi radians in one oscillation on a sin curve

 

[sophiecentaur]

consider a single photon traveling in a straight line. it has energy, and it is oscillating through a wave form.

the particles in the string don't get given the energy all at the same instant, which is why parts of the string are in different parts of the wave. a wave travels through a medium, like you said, by passing on it's energy.

when i say 'time period' i am referring to the time it takes for the particle to move through 2pi radians, not the time at which that particle was given energy.

if you drop two identical balls onto a surface, at different times, they won't hit the ground at the same time, nor will they reach their highest point at the same time, but the time it takes for them both to do this, will be the same.

If we are dealing with a wave on a string is REALLY can't be helpful to introduce Photons into the situation. Who ever said that photons are "oscillating through a wave form", anyway? Can we please stick to the classical wave stuff until we get it properly sorted?

@Celluhh
Remember that a wave (to be a wave) varies in distance and time. Each particle on your string (or whatever) goes through a complete cycle of motion in the same time as every other particle - there is just a slight delay for each successive particle on the wave path.
A freeze frame picture of the wave as it travels will show you the spatial form / wavelength and watching just one point to see how the displacement varies in time will tell you the frequency.

If you draw a wavy line on a long piece of paper and move it in front of you, the line goes up and down at the frequency of the wave and the space between identical parts of the wave is the wavelength. The speed that the wave is traveling will be the frequency times the wavelength - (how many waves pass in a second times their length).

 

[lntz]

i was trying to create an example where there is one object oscillating without considering what happens to other particles.

in hindsight - that was a bad choice

 

[Celluhh]

@ intz I knew what you were trying to get at so it's ok. @sophiecentaur if I understand you correctly you are saying we can consider the freeze frame picture of the wave to be as if the complete wave is formed in the given period although there is a time lag between the movement of particles?

 

[Celluhh]

To be perfectly frank, I know how to use the terms to find myself the answer. But what I want to know is not how to find the answer based on formulas, but truly understanding
How the answer is derived. which is why I think too much most of the time . And why I can't understand the simple school question I posted in my first post.

 

[Bob S]

It is perhaps useful to first understand how energy is transferred between kinetic and potential energy in the classic pendulum (force = F = mg), then with a mass on a coil spring with a F= -kx restoration force, then finally with the tension on a string creating a restoration force and a traveling wave.

 

[lntz]

is it safe to assume that all the waves we are considering are isochronous?

to me it looks like you're moving into SHM, but is this a decent explanation of how a wave behaves?

 

[sophiecentaur]

i was trying to create an example where there is one object oscillating without considering what happens to other particles.

in hindsight - that was a bad choice

Yes. Particularly because there is no particular evidence that a 'photon' actually oscillates.

 

[sophiecentaur]

@ intz I knew what you were trying to get at so it's ok. @sophiecentaur if I understand you correctly you are saying we can consider the freeze frame picture of the wave to be as if the complete wave is formed in the given period although there is a time lag between the movement of particles?

At one instant of time, all the particles are in different places - along the profile of the wave (Think of a photo of water waves). Each one is oscillating a bit earlier in phase than its downstream neighbour and a bit later than its upstream neighbour.
The definitions of wavelength and frequency support this idea.

 

[sophiecentaur]

is it safe to assume that all the waves we are considering are isochronous?

to me it looks like you're moving into SHM, but is this a decent explanation of how a wave behaves?

Not all waves are based on SHM movement of the 'particles' but it is easier to start with such waves. Using a different waveform just makes things more complex.

 

[lntz]

maybe oscillates was again not a great choice in words.

i am no expert, and still a student, so i am very much still learning.

what is a better word for describing a photons motion then? (sorry for taking this offtopic slightly)

 

[Bob S]

is it safe to assume that all the waves we are considering are isochronous?

No. They are all the same frequency only.

to me it looks like you're moving into SHM, but is this a decent explanation of how a wave behaves?

Yes. Using the string example of the OP, each segment of the string has mass, and is undergoing simple harmonic motion in the transverse dimension, with the string tension providing the restoring force. No segment "knows" that the SHM is actually part of a traveling wave.

So why then is there a traveling wave on the string? Because the transverse restoring forces on the two ends of the segment are different (even though the tension is the same).

String segments can be arbitrarily small.

 

[sophiecentaur]

maybe oscillates was again not a great choice in words.

i am no expert, and still a student, so i am very much still learning.

what is a better word for describing a photons motion then? (sorry for taking this offtopic slightly)

A Photon is not something that can be described in simple terms like a particle that wiggles from side to side on its way from A to B. It is massless - so it's not like the other 'particles' we're used to dealing with and it travels at c. If it were to be wiggling from side to side it would, actually, need to be going FASTER than c in order to go the same distance because it would be traveling further. It's a difficult one.
But, as you say, this thread isn't the place to discuss it and I think you'll see that it doesn't really help in getting to grips with classical waves on strings or in air or wherever.

 

[Celluhh]

At one instant of time, all the particles are in different places - along the profile of the wave (Think of a photo of water waves). Each one is oscillating a bit earlier in phase than its downstream neighbour and a bit later than its upstream neighbour.
The definitions of wavelength and frequency support this idea.

Yes I share the same sentiments as you but I don't get how the definitions if wavelength and frequency support this idea. Also, I still do not understand how the period is the time taken to create one complete wave when the above stated is actually true.

 

[sophiecentaur]

Perhaps, if you tried to show it wasn't true, then you'd find that you can't. It all makes such good sense to me. ;-)
Do that thing with a wavy line on a long piece of paper, moving to the right. It may help; the picture is the wave in space and the bobbing up and down is the time variation. The two variables are separate and I think you are connecting the two in your mind.

 

[lntz]

if you are studying physics in, then i really do recommend that you speak to a teacher/lecturer about this.

it is not easy to explain clearly in words, without the use of diagrams.

 

[Celluhh]

Yup I plan to ask my teacher when I go for tuition! Anyways thanks guys for helping

 

[Celluhh]

Bob s, can I trouble you to explain shm in a simpler manner? I have
Not touched on that topic yet but if it could help me
In understanding , I'm interested.

 

[Bob S]

Yes I share the same sentiments as you but I don't get how the definitions if wavelength and frequency support this idea. Also, I still do not understand how the period is the time taken to create one complete wave when the above stated is actually true.

Bob s, can I trouble you to explain shm in a simpler manner? I have
Not touched on that topic yet but if it could help me
In understanding , I'm interested.

It might be useful to first look at what produces the wave velocity v in a string or other long connected line of masses. When the wave equation for a vibrating or plucked string is derived, the wave velocity for a string of mass ρ kilograms per meter and longitudinal tension T Newtons is
v=\left[ \frac{T}{\rho} \right]^{1/2} \text{ meters per second } The string mass per unit length ρ is equivalent to a mass m on a simple spring, and the tension T Newtons is equivalent to the restoring force F on a compressed or extended spring. The net transverse restoring force on a unit length of string is due to the fact that at every moment in time, the transverse restoring force at point x is approximately F_x = T tan(θ_x) because the string has a slope tan(θ_x) with respect to the unplucked string, so for a segment of string δx, the net restoring force is
F=T\left[ \tan\theta_{x+\delta x}-\tan\theta_{x} \right]
This is because the string is flexible, and there is curvature between x and x + δx. Thus each segment of string undergoes SHM (simple harmonic motion).

In a simple mass on a spring, the restoring force is F = -k(y-y_o) = m d²y/dt², leading to an angular oscillation frequency ω = (k/m)^1/2 radians per second.

 

[Celluhh]

Ok I get the gist of it, but isn't this more like telling us how a transverse wave is formed??ok pardon
Me for my ignorance I may have inferred wrongly

 

[lntz]

do you understand about standing waves on a string, and where abouts the nodes and antinodes must be? this is a first step to understanding waves on a string

 

[Celluhh]

Huh really? No I don't... My teacher didn't mention anything about them.

 

[Celluhh]

Hold on I think I was taught just that I wasn't taught the term

 

[lntz]

the general idea is that you can only fit certain wavelengths on strings of certain lengths.

at either ends of the string the waves amplitude will be a minimum (node), and at certain intervals along the string, the wave will be at a maximum (antinodes)

to have a wave on a string you must have atleast 2 nodes and 1 antinode, from there you can create shorter and shorter wavelengths by 'squeezing in' more nodes and antinodes.

2 nodes and an antinode would be half a wavelength.

 

[Celluhh]

Ok, it seems I haven't learned this yet. But how is this related to the period?

 

[lntz]

this relates to wavelength.

i don't know if anyone has made the point yet that time period is = 1/frequency.

that is what the time period is. so your questions about how can 1 wave be completed in the same time period as all the other parts of the string, seems strange. unless your frequency is changing, the time period is constant.

 

[sophiecentaur]

You can get traveling waves on strings too as long as the far end can move and dissipate (absorb) the energy reaching it. Waffling a long rope on the ground can produce a convincing traveling wave.
But, as has been said, most waves that we see on strings are standing waves in which the energy travels to the ends and is reflected many times, building up into a standing wave pattern.
Standing waves are usually the next step on from being taught about traveling (progressive) waves.

 

[Celluhh]

this relates to wavelength.

i don't know if anyone has made the point yet that time period is = 1/frequency.

that is what the time period is. so your questions about how can 1 wave be completed in the same time period as all the other parts of the string, seems strange. unless your frequency is changing, the time period is constant.

It is not that I do not know the definition of period, it is because I know it that I am asking about it. I am tryin to visualise the definition, .

 

[sophiecentaur]

Does the definition need to go further than saying that the period is the time for one cycle to be completed at any fixed point in space?
Likewise, the wavelength is the space between identical points on the wave at a given time.

You can't get much more succinct than that.

 

[Celluhh]

Does the definition need to go further than saying that the period is the time for one cycle to be completed at any fixed point in space?
Likewise, the wavelength is the space between identical points on the wave at a given time.

You can't get much more succinct than that.

Yeah, why any fixed point, they don't even receive energy and start moving at the same time, do they have the same speed?

 

[sophiecentaur]

Yeah, why any fixed point, they don't even receive energy and start moving at the same time, do they have the same speed?

I don't exactly understand your question but the wave takes time to travel so the displacement at different points on the wave will be different. This is obvious when you look at a wave in action. A ball, bobbing on the sea moves away from its highest position and returns, at regular intervals (1/frequency). Balls in other positions are not at the same part of their cycles. If what you seem to suggest were true then the whole of the sea would be going up and down at the same time.

I say again that, to get a handle on this, you can draw a wiggle on a piece of paper and move it past your eye. You can see the wavelength (measured on the paper) and you can follow the variations of 'height' as it goes past. No fancy computer simulation - just a piece of paper, a pen and a brain needed.

 

[Celluhh]

Uh I don't think you understand my question. Precisely because I understand how displacement of particles at different points of the wave is different, which is why the wave is formed in the first place, that I am wondering why, when the wave travels, or more specifically, energy is transferred from one particle to the next and the particles start moving consecutively, that they actually manage to all complete one
Oscillation in the same period to form one complete wave in that one period. Unless of course they are all moving at different speeds, or they all start moving at the same time, which is impossible.

 

[sophiecentaur]

Ah, I think I've got it now. Well - all the 'particles' involved are in identical situations to the others (assuming a homogeneous medium) They can all be modeled as a chain of identical masses, coupled together by identical 'springs' (all non-EM waves boil down to this basic model). Energy is passed along the chain of particles at a rate that depends upon the 'masses' and 'spring stiffnesses'. They will all respond the same and the forces acting on them will be the same - just a bit later as you look along the wave.
The time taken for one particle to get energy from its earlier neighbour and deliver it to the next one is what defines the speed of energy transfer. Each one is being dragged to follow one neighbouring particle and is dragging the next one in the chain. The more stiff the spring is, the closer the movement of each particlal follows its neighbour (higher wave speed), for a more sloppy spring, the delay will be greater and the wave speed will be lower. The frequency of the oscillations will all be the same and determined by the frequency of the source of the wave.

I could suggest that you try to show that they would behave in a different way - in order to justify your reservations. If you can't show that the standard model is not true then that would be a reason to assume that it could be true.

BTW, what actual type of wave are you using 'in your head' when you are visualising all this?

 

[Celluhh]

A transverse wave.

 

[Bob S]

Uh I don't think you understand my question. Precisely because I understand how displacement of particles at different points of the wave is different, which is why the wave is formed in the first place, that I am wondering why, when the wave travels, or more specifically, energy is transferred from one particle to the next and the particles start moving consecutively, that they actually manage to all complete one
Oscillation in the same period to form one complete wave in that one period. Unless of course they are all moving at different speeds, or they all start moving at the same time, which is impossible.

Here is a youtube video of a traveling wave on a long rope:



Every segment of the rope is oscillating up and down at the same frequency (and the same period), but each adjoining segment has a slightly different phase, so the wave appears to be traveling.

 

[sophiecentaur]

@ celluh Which particular 'transverse wave'? The problem is that we come across very few progressive transverse waves.
Whether transverse of longitudinal, the same arguments all apply because you always have a displacement of some sort and a restoring force.

 

[sophiecentaur]

Here is a youtube video of a traveling wave on a long rope:



Every segment of the rope is oscillating up and down at the same frequency (and the same period), but each adjoining segment has a slightly different phase, so the wave appears to be traveling.

That movie is quite good but the wave suffers from severe attenuation because it is dragging on the ground. But at least it is a truly progressive wave as there is no reflection so standing wave is generated.

The best progressive waves to study are on water - the only snag being that they are not transverse waves but a combination of both transverse and longitudinal. If one accepts that then all the basics are there and easy to watch and to visualise.

 

[Celluhh]

i consulted my teacher today and one sentence she said really woke me up.She said, the definition of period is the time taken for a particle to complete one oscillation, and it is also the time taken for one wave to be completed. However, the important thing to note is that although every particle completes an oscillation in the same time period, they do not complete their period at the exact same time, the particles are all in different phases of their oscillation with different speeds when the wave is completed. the definitions of period are just telling me that the time taken to complete one wave is one period and the time for one particle to complete one oscillation is also one period.
perhaps its the last sentence that made me accept the fact that i was complicating things too much.

So, my next question is, how do the particles "know" how to form a complete wave in one period, and make the wave periodic? ok, here i go again.

 

[sophiecentaur]

Particles need to "know" nothing. It is entirely the other way round. The result of how each (identical) particle behaves as it is pushed and pulled by its neighbours is what forms the wave and the mass / stiffness involved, determines the speed of the energy passing through ( the wave speed).
In a medium with almost zero mass particles and with very high stiffness there is a very short lag in passing the effect of a disturbance. The wave would not be 'visible' because there would be no apparent difference in their position. Wave speed would be ' infinite' (very high).