# Why can't amplitude make a tranverse wave faster

1. May 27, 2014

### trill

Why is the speed of waves in a medium fixed?
I'm trying to conceptualize this, but I can't.
I imagine a long piece of chain on the ground, of course made up on individual links.
If I yanked on the first link by lifting it up, it wouldn't in act a force on the second link until it made tense contact with it. But If i yanked up the first link incredibly fast (ex: 100,000 mph) shouldn't the
first link very quickly (that is in time) force the second link up , which in turn forces the third link up that much faster.

Can anyone help me understand?

2. May 27, 2014

### SteamKing

Staff Emeritus
I'm afraid you have some misconceptions about transverse waves.

For instance, water waves travel at different velocities depending on the wavelength, not the amplitude. Amplitude is independent of wavelength and has no effect on wave velocity. A water wave of a given wavelength can have many different amplitudes (not all at once, of course), but there is an upper limit to the ratio of wave amplitude to wavelength. When the wave amplitude exceeds this limit, a wave crest is produced, and the wave motion is no longer quite so regular.

3. May 27, 2014

### trill

I'm speaking of the fact that the speed at a which a wave can travel in a particular medium is fixed. I'm specifically referencing a wave on a string like material.
I also messed up by asking why amplitude can't make the wave travel faster when I should have asked why the frequency (or in my example the speed at which I yank the first link) can't make the Wave travel faster in the medium.

4. May 27, 2014

So you are asking if the frequency of the wave can make it move faster?
$v=f \lambda$ Where $v$ is velocity, $f$ is frequency , $\lambda$ is the wavelength.
If the frequency is increased while the wave length remains constant, then it will move faster.

5. May 27, 2014

### Maxo

I think what trill is asking (correct me if I'm wrong) concerns his analogy with yaking chain lying on the ground. The question then, when yanking the chain up and down at one end, if one does that faster (higher frequency) will then also the wave propagation speed increase? Or will the wavelength change?

6. May 27, 2014

### sophiecentaur

The speed of a wave through a medium, whatever it is, depends upon the density or amount of mass per unit length involved and the stiffness or modulus of the medium, chain, string. etc. If the medium is linear (force is always proportional to the impressed force or pressure) then the speed will be independent of amplitude. However, if the material is not totally linear (if it hardens up or goes softer when stretched a lot) then the speed of the wave can change with amplitude. So the intuitive feeling that getting violent could affect the speed, is not totally groundless.
Non-linearity can also cause other frequencies to be generated, which makes things more complicated.

When waves break on the sea shore, it can be explained in terms of the change in speed with depth and the troughs travel slower than the peaks, causing the waves to tumble over themselves. Shallow water waves are pretty complicated things to deal with though.

7. May 27, 2014

### trill

But doesn't my thought experiment also apply to a rope? and if it does, isn't the speed of a wave in a rope always the same?

8. May 27, 2014

### sophiecentaur

Speed on an ideal string is not frequency dependent. That's standard textbook stuff. You have a linear medium too.

9. May 27, 2014

### Maxo

So in other words increasing the frequency on the string - for example holding one end of the string and yanking it faster - will instead decrease the wavelengths, since the speed remains constant.

10. May 27, 2014

### sophiecentaur

11. May 27, 2014

### trill

I hate to be repetitive, but what about my though experiment?
a string with particles. I imagine if that if I lifted up the first particle at 1 mile and hour, the second particle wouldn't move up until it feels a force from the first particle which will happen when it become taut or tense with the first particle. And so on with the third, fourth, five particles.

But if I shot the First particle up at 100 MPH, the first particle would shoot up, and almost instantly stretch out and pull the second Particle, which would almost instantly pull the third, etc. Would the Wave would be travelling faster?

12. May 27, 2014

### sophiecentaur

One thing I can say that may help you is that the period of a simple oscillation is the same, whatever the amplitude. Galileo came to this conclusion when he observed the behaviour of pendulums. In your scenario, however fast you jerk the string, the times involved are the same (hence the speed of wave).
If you are modelling your wave as a set of masses, connected by strings then that is a common model that's used. It is an approximation to the model of a continuous string. Your sort of wave is more or less the same as a continuous string until the number of masses per wavelength becomes small and they part company. Trying to analyse this sort of think with just words and arm waving really doesn't get you far because it's all down to the Maths, I'm afraid. All you can do is accept what you have been told about the result or learn about the Maths involved. You can't jump into this sort of thing half way through and expect to get a lot out of it.

Here is a link that describes the sort of system you are thinking of - except the oscillations are longitudinal rather than transverse - but there is very little difference in the result. Here's another one, which looks at the standing wave you get on a string loaded with masses.

13. May 27, 2014

### dauto

Not for an ideal string. You would get a higher frequency but the same speed.

14. May 28, 2014

### Maxo

15. May 28, 2014

### sophiecentaur

So you want me to repeat what's on that link? Why? Who's too lazy to read a link?
Until you are paying someone for answers, you have to accept what you're given. You're on your own now afaiac.

16. May 28, 2014

### Maxo

In case you missed it, this is a forum for helping each other. If someone asks a simple question, you are not supposed to answer something like "try reading this 1000 page book and you will find the answer". In the same way, the link you provided have tons of other information, equations etc. that are only confusing when wanting to just answer a very simple question.

I will rephrase my question:
When increasing the frequency on the string - for example holding one end of the string and yanking it faster - this will decrease the wavelengths, since the speed remains constant. Is this a correct analysis?

17. May 28, 2014

### ZapperZ

Staff Emeritus
"Helping" is a broad term. Giving you fish is "helping", but the next time you are hungry, you will need to find another person to give you fish.

What you were given was instruction in how to fish, so that the next time you are hungry, you will know what to do on your own! The link you were given at Hyperphysics is very useful, not only to address your question, but as a resource, so that the next time you have a similar problem, you know where to look! That is a an extremely valuable form of helping, and it is more useful than just telling you the answer!

We encourage users to include references/sources in their responses with the hope that those who truly wish to learn can look at those sources to understand things further. So please do not denigrate anyone who not only spent time responding to your post, but also provided valuable references for you to look at and study! You should be thanking them, not complaining at them!

It is also bad form telling someone who has been here way longer than you on how this forum is run.

Zz.

18. May 28, 2014

### Maxo

Using your own analogy your premise incorrect. You are assuming everyone has to be a fishermen, ignoring all other possible reason for wanting a fish. For example, someone who doesn't even want to eat fish, but wants one for dissecting it, for whatever reason. Or a completely different reason. There are tons of possible reasons why a person could want a "fish" without needing to learn everything there is to know about "fishing".

I'm not saying it's bad to give resources. I actually agree with you that it can be extremely good and useful. But you can't say that "giving resources" per definition is always a good anser. As you know everything is relative and a good answer must definitely be put in relation with the question. Sometimes the best answer to a question is to simply give a short, concise answer, if that's what is asked for. Perhaps the one who asks doesn't have time to go in to the subject deeper, but just want a detail clarified. Then giving a whole page of other stuff is NOT a good answer.

19. May 28, 2014

### ZapperZ

Staff Emeritus
But that isn't what you were given! You were given an explanation, and then you were given places where to check (or double check) what you were given! This is what it means to LEARN, i.e. most of the "dirty work" has to be done by YOU and no one else! The only way to learn how to dissect a fish is to actually do it yourself, not to ask someone else to do it for you!

I can turn this around and say that you want to be spoon-fed. We definitely do NOT do that here, since we are in the mood of telling others on how this forum is run.

This line of discussion will end here. You are welcome to post your complaint on this policy in the feedback forum. Otherwise, this is off-topic to the thread.

Zz.

20. May 28, 2014

### sophiecentaur

Wasn't the question answered in posts 6 and 8?