# A Impacted on a Surface wave of a tension-ed Anchor cable

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1. Nov 15, 2017

### Tom79Tom

I'm trying to figure out what happens to a tension-ed anchor line when encountered by a surface wave (transverse and longitudinal )

Assuming a 2 dimensional view, or that the cable is sufficiently wide that the wave cannot go 'around it' what happens to the path and speed of the surface wave .

Is a portion of the wave encountering the boundary reflected by Snells way from the boundary? (upward) Is the reflection coefficent higher the higher the tension in the cable ?

As speed is directly proportional to tension Does the portion transmitted to the anchor cable travel along its length at faster speed .

Does the transmitted portion also transmit thru to the water below returning to the same speed?

Is the outcome related to only one component transverse or longitudinal or is it the same ?

2. Nov 16, 2017

### tech99

Isn't this the same action as at a beach?

3. Nov 16, 2017

### A.T.

So it's actually a flexible barrier?

4. Nov 16, 2017

### Nidum

Is this question really about what happens to the tension in the anchor cable when the wave hits the boat ?
The interaction forces between the wave and the anchor cable are minute compared with the interaction forces between the wave and the boat .

If though we take your question literally then a moving column of water is pressing down on a flexible sheet with an uncertain fixation at the boat end . Working out what happens in that case would take forever since there are so many variables involved .

5. Nov 16, 2017

### Tom79Tom

Yes that's probably a good description! but under tension... i'm trying to understand how the surface wave (at depth) would interact with it . without the tension i would see the sheet just transmit the wave ..i might be wrong ?

No i am not really interested in the boat, its more an analogy- it could be replaced with a post etc that fixes the tension in the otherwise flexible sheet? Does that make it simpler ?

6. Nov 16, 2017

### Nidum

Assuming that there is free flow of water between the upper and lower sides of the sheet then at slow speeds this is just a point load on a washing line type problem .

At higher speeds there will be horizontal and vertical load components . These will require a hydrodynamic analysis to evaluate . No easy but probably do-able for an idealised version of the problem .

7. Nov 16, 2017

### Tom79Tom

If it was sufficiently permeable wouldn't the wave be allowed to transmit ? i'm assuming it would be impermeable to have any effect ? The speed range in question for ocean waves is 10-20 meters per second ? is that slow speed or fast?

8. Nov 16, 2017

### Nidum

That's the third version of the problem in as many posts .

Please let us have a more definitive description of the problem that you are trying to solve .

9. Nov 16, 2017

### Tom79Tom

I haven't revised it, . I started with the statement that the cable was under tension and the wave couldn't go around That remains the scenario i still wish to explore. i'm not sure what else i can add to the description
The examples i can find about reflection from an impedance discontinuity all talk about changes in density but rarely (never) talk about the action of a surface wave encountering tension. Its like a surface wave hitting a really wide guitar string underwater

10. Nov 16, 2017

### tech99

In principle I think it is like a sound wave hitting a diaphragm. It will be reactive above and below resonance, where it will reflect part of the energy, and will be nearly transparent at resonance. However, the water is a dense medium, so I think the membrane will be strongly coupled to it and its own resonance will be largely damped out, making it nearly transparent at all frequencies. The tension of the membrane will be negligibly small compared to the moving mass of water.