Ripple tank dispersion

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Summary:

Ripple freq effect on refraction angle

Main Question or Discussion Point

Consider water waves refraction in a ripple tank. What happen if we increased the ripple frequency. I mean the refraction angle would change or not? Also, propagation speed will change or not?

I had seen a photograph in PSSC Physics. According to that, the refraction angle was reducing if we increase the ripplle frequencey. I cannot find any other reference to this situation.

One more time, does ripple frequency change the propagation speed?
 

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  • #2
phinds
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One more time, does ripple frequency change the propagation speed?
Why would it?
 
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Because refraction angle is changed. So the speed also. According to Snell Law.
 
  • #6
berkeman
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Did you see the part about how the wavelength of water gravitational waves is related to the depth of the water? When you use a forced ripple tank to generate short-distance waves of an arbitratily small wavelength, that is a different situation. Do you have a ripple tank that you can try this in?
 
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  • #7
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Unfortunatly. I don't have a ripple tank.

As I understand, shallow waters aren't dispersive. When it comes to deep water, it is dispersive. In deep water, the group velocity is equal to half the phase velocity. In deep water the phase speed increases with the wavelength, and with the period. Since the phase speed satisfies cp = λ/T = λf, wavelength and period (or frequency) are related.

So, in deep water (the depth larger then 1/2 of wave length) phase speed can change with frequency isn't it? Then, refraction angle will change with ripple frequency.
 
  • #8
sophiecentaur
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Unfortunatly. I don't have a ripple tank.
Are you planning to have one available or is this a thought exercise?

The amount of refraction depends on the change in wave speed. In deep water (Depth is more than one wavelength) the speed is only dependent on wavelength. In shallow water, the speed doesn't depend on wavelength and it is totally dependent on depth.

The maths of this is horrible, if you don't like that sort of thing so avoid thinking about what happens in 'moderate depths'. The formulae at the bottom of this reference, sum it all up. A practical demonstration of all this can be seen on any shelving beach with waves arriving at an angle to the normal. You can see small ripples moving very slowly, compared with the main set of waves arriving (deep water condition for the short waves) a range of shorter waves can be seen to travel at different speeds. You can see the longer waves being bent more and more towards the beach as the water gets shallower and, eventually, they arrive almost at right angles to the shore as the depth tends to zero. Longer and shorter waves tend to behave the same way near the shore. No equipment but eyeballs needed here and you get a nice day out at the seaside, too.

In a practical (school-type) ripple tank, the depth of water is such that what you see is the 'shallow' condition. The wave making device tends to be a bar that is attached to an eccentric pulley on a small motor. This is a poor system for exploring a range of frequencies. It's all held up by rubber bands and you cannot get the motor make the bar oscillate in the water at any frequency other than the one the maker wants you to. If you use a better 'actuator' you can make waves of many frequencies and take it into the 'deep water' condition. Also, a stroboscope can allow you to see the wave patterns, frozen.

EDIT: PS I did a lot of experimenting with a tatty School ripple tank and used a signal generator to move a piston at a range of frequencies and a strobe. I showed the other staff just what it would do but, unfortunately, the setup was too hard to drive for yer average secondary Science teach and I never got to present it to kids. I then realised that 'too much' Science is not always a good thing in teaching.
 
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  • #9
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Thank you. No, I won't. Just thought exercise.

That pdf file is great. Thanks for that. And yes, I don't need horrible equations.

I think, understood it. Just one question. Let's consider a giant vibration tank with a sufficient depth and a constant depth. Even a motor that can vibrate at a fixed frequency is available with it. With these conditions, we can create deep water waves with a single wavelength, right? I ask this for the following reason. As I originally wrote, the PSSC Physics book wrote that the angle of refraction varies with frequency, and the speed also changes. But the book did not mention the depth of the water. Perhaps this can be explained in a similar way to the paragraph you just added. Maybe.

With this opportunity, I wish everybody here healthy days.
 
  • #10
sophiecentaur
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But the book did not mention the depth of the water.
For gravity waves, the only thing that can alter the speed is the depth. The frequency is the same along the whole path of the wave. Aamof, trying to understand wave behaviour is a lot harder when you try to start off with gravity waves because they involve displacements which are both longitudinal and transverse and the motions are not sinusoidal. A simple transverse wave on an ideal string or a longitudinal wave through water or air is probably the best way into the subject. Refraction, of course, needs two or three dimensions so sound and light are good directions to look. Only when you have all that sorted out should you try gravity waves.

Check that your PSSC book is actually referring to gravity waves when it says that refractions varies with frequency. Light through glass is subject to dispersion and that could be what they are talking about.
 
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  • #11
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For gravity waves, the only thing that can alter the speed is the depth.
We said that the propagation speed in deep water depends on the wavelength. If we increased the frequency, the wavelength will be shorter. So the speed will also change. This is not wrong, I suppose.

Check that your PSSC book is actually referring to gravity waves when it says that refractions varies with frequency. Light through glass is subject to dispersion and that could be what they are talking about.
It was the water waves mentioned in the book. Anyway, what I'm trying to understand is just the separation in the water waves.
 
  • #12
sophiecentaur
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If we increased the frequency, the wavelength will be shorter. So the speed will also change. This is not wrong, I suppose.
I can see you are trying to nail this down but gravity waves are not simple (and not the best waves to start your learning with). There are two regimes - as mentioned above. There will be no diffraction in deep water, which is where the speed is frequency dependent. It is in shallow water that the dispersion comes in and in shallow water, the speed is dominated by the depth.

If the PSSC book suggests otherwise then I would take issue but, of course, I would first make sure that you have actually got their message right. If the book is trying to teach you about waves by using gravity waves as an example then I would wonder about the quality / context. If you have dived into their treatment half way through then you should go back to the start of that section. Otherwise you should go to another source and see if you get the same message there.

On the topic of large scale 'ripple tanks', there are a number of marine science research establishments that use the sort of tank you are talking about. See this link and you will realise it's an expensive business!!
 
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  • #13
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First of all, let me say that this book was at high school level and that it was first published in 1959. (https://en.wikipedia.org/wiki/Physical_Science_Study_Committee)

The book doesn't talk about the depth of the water. It states that when the frequency increases, the angle of refraction decreases and this is similar to the optical refraction and dispersion that we will see in the next topic.

Undoubtedly, an idealization must have been made in this context. As far as I have learned, the subject is more detailed than it appears in that book. But I am looking for a short answer to the question of whether the propagation speed changes when the frequency of vibration changes. Of course, when answering, we can specify the conditions. Or, what do you think is the answer to the question of whether the wave velocity changes when frequency changes?

Thank you also for the video link. I would love to go there and do some experiment :)
 
  • #14
sophiecentaur
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this book was at high school level
A sixty year old book is hardly the best one to use as you have no idea about how suitable it is and there will be no reviews of it to tell you. It's of the same vintage as books that I used in school and their style was very formal and didn't always present the Science in a friendly way. The actual Physics of this has been known for well over a hundred years but the presentation in your book could be confusing you. How you describe what you have read is confusing me. The problem is that you do not want to get into the maths of it and the whole subject relies highly on maths. The potted version I gave you is the bottom line and that seems to go directly against what you think that book says. So the only way is for you to try to find a non mathematical treatment of the topic of gravity waves - which could be over - simplified and badly summed up.
 
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  • #15
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Thank you. You are right. The relationship between frequency and speed in the book is completely opposite with our current knowledge. And I don't want to get into the maths of it. Because I took quite a break from that mathematics. It's hard to come back. Moreover, there are no people in front of me to tell about. I wanted to find the answer to the question of what the propagation speed depends on and to say whether it depends on frequency or not. Anyway. I think it is best to pass superficially.

Best Regards
 
  • #16
sophiecentaur
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Best to go and watch the real thing at the seaside - covid 19 permitting.
 
  • #17
sophiecentaur
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The relationship between frequency and speed in the book is completely opposite with our current knowledge.
Haha. Our "current knowledge" was right, even in those ancient times. It was the writer of the paragraph in the book who was wrong yet he actually would have known the right answer. Problem with texts with many different authors can be that things get missed during the vetting because some of the contributors are very last minute with their bits. One single painstaking author can be more careful but all textbooks have at least one thing wrong in them. (There's a challenge!!!!)
 

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