# What happens to a shear wave at a solid/fluid boarder

1. Dec 20, 2012

### Nomator

Hey people, I am embarrassed and I tried hard to find an answer on that one.

I know that shear waves only travel in solid media but what happens on the border from a solid to a liquid. Does the shear wave cause a longitudinal wave?

I found an article where a graphic shows that behavior but wherever I look for a text description what happens and why I don't find anything.

I would really appreciate it if somebody can tell me if I am right or wrong or even better has a quote which proves that behavior.

You can find the article here and the graphic is figure1:

http://www.cnde-iitm.net/Published%20Papers%20pdf/1996%20EFFECT%20OF%20VISCOSITY_15.pdf [Broken]

Last edited by a moderator: May 6, 2017
2. Dec 20, 2012

### sophiecentaur

Hi and welcome.
If the wave can't propagate across an interface then it will be reflected. In fact at any interface where the speed or some other characteristic changes , some energy is reflected. The principle of conservation of energy always applies (one way or another) and many explanations are based on it.

I just had an idea. If the shear wave hits the interface at an angle, the longitudinal component of the oscillations can couple into the liquid.

3. Dec 20, 2012

### Nomator

Thanks for the quick reply. Do you think the angle is a requirement?

It's just funny that I don't find anything on the web about a behavior like this. I asked a prof. and he said yes but i don't know if he thought about it deeply...

4. Dec 20, 2012

### sophiecentaur

He was probably considering his Christmas Departmental Lunch!

The longitudinal component of the wave would be proportional to the sine of the angle of incidence (would it not?). In addition to that factor, you will have the usual reflection coefficient, involving the two velocities. I think this link would tell you all you need but there a many others. That link doesn't discuss transverse waves but I think you could just deal with the longitudinal component and get the right answer (if the solid medium is isotropic and linear)
If you need to produce any work about this then I am sure that approaching it this way would be quite acceptable. You had a go and in a valid way!

5. Dec 20, 2012

### Nomator

Ok i get the point that the energy from the transverse wave has to get somewhere when it is not reflected. The reflection theories are no problem.

I looked at this article again now and i think it pretty much solves my problem I sometimes need a to describe my problem and talk about it to really understand what I am about to do.

The only thing what I don't get is the longitudinal component.

The article is attached.

Thanks so much so far if you want to go on explaining the longitudinal component to me more I would be happy but that would be the "top of the muffin".

#### Attached Files:

• ###### G8DFur-1996 EFFECT OF VISCOSITY_15.pdf
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6. Dec 20, 2012

### DrDu

Whether or not a longitudinal wave emerges depends on the angle of incidence. I.e. for perpendicular incidence of the shear wave, no longitudinal wave will be created.

7. Dec 20, 2012

### sophiecentaur

You need the component of the original transverse displacement in the solid that is not parallel to the interface (because that won't couple into the liquid). i.e. you want the Normal component to the interface - which is A sinθ, where A is the Amplitude of the transverse wave and θ is the angle of incidence. It is zero for normal incidence (as a check).

I read that article (briefly). The diagram at the top of p818 seems to tell the story and they mention Snell's Law, which figures. It makes sense to me - but if I actually wanted to do some calculations and predictions it might not be so simple!
.