Interference of waves is something often taught either using light as a practical example, or without a practical example. Here I want to show a couple of observations as well as a simple experiment.
When talking about waves, it is often difficult to explain that wave heights of different components of a wave field can be added to each other to give a resulting wave field, but that each of those components continues to travel with its own direction and speed and comes out of the wave field basically unaltered. Students learn about constructive, destructive and complex interference (see image below), but it is hard to realize that those interactions are only momentary and that waves come out on the other side without having changed their shape.
Constructive, destructive and complex interference of waves.
In the ocean or on lakes or rivers, you are sometimes lucky enough to observe interference of waves. At a lighthouse in the southwest of Iceland, I took the image below: Two distinct fields were meeting each other at an almost 90 degree angle, interacted and left on the other side still clearly recognizable.
Two wave crests meeting at approximately 90 degree angle.
The waves met, interacted, and left the area of interaction. Watch the movie below to get an impression!
Of course, it is very hard to plan your course such that you happen to observe this out in the “real world”. But interference of waves is so easy to set up, in any pool or tub of water! If your body of water is very small, you can even create waves with only one source and have the reflection from a wall interfere with the “original” wave (actually, you’ll probably have to, because otherwise the reflected waves will mess with the ones you are creating).
Feet tapping in the lake in Ratzeburg to create a pattern of wave interference
Check out the movie below! This is so easy to do, yet so impressive if you have never observed it before.
P.S.: This text originally appeared on my website as a page. Due to upcoming restructuring of this website, I am reposting it as a blog post. This is the original version last modified on November 27th, 2015.
I might write things differently if I was writing them now, but I still like to keep my blog as archive of my thoughts.
Bergen had it’s two days of allocated summer during the weekend of 22 – 23 July 2017 and Elsa and I decided to – in true Norwegian style – take advantage of the rare occasion and go for a hike. A colleague of mine has a “hytte” near Langhelle and had invited us over for the day. So we each packed our “matpakke”, hiking boots and got on the train from Bergen to Vaksdal, where my colleague had arranged to pick us up.
Anyway, long story short, apart from the spectacular view over Sørfjorden, I thought that the following would make you smile. Pointed it out to Elsa and, as if on cue, in unison we said your name out loud.
I’m afraid the resolution is not that great though – had to zoom quite a bit to capture what was much more clearly visible with the naked eye.
I’m including a map to show where it is. The arrow indicates more or less where we were standing when I took the picture; the circle around the area. Opposite Vaksdal, on the western bank (does a fjord have a “bank”? What’s the correct term? “Wall”?) of Sørfjorden is Olsneset and the little isle, Olsnesøyna, you see in the pic. There’s apparently an “open air” prison on the island. Not a bad place to be incarcerated!
One of the wave trains was made by the little ferry that runs to and fro between Vaksdal, Olsnesøyna and Osterøy.
I’m sure that the readers of your blog would also enjoy the pic, so please feel free to use it.”
I obviously love it when my friends think of me, but it makes me even more excited when they think of me in connection to cool stuff related to water and send me pictures. But clearly the first thing I had to do upon receiving this email was to try and interpret the picture.
So I know there were two ships causing the waves. But which way were they going? So my first guess was two ships going in opposite directions. I’ve drawn the edges of their wakes into the picture below (ship 1 green, ship 2 red), the ships would now be more or less at the pointy end of each of the Vs.
But then I noticed the waves that I drew in blue in the picture below. Could they be part of the wake if a ship? And could that white spot in the picture actually be said ship? Then ship 1 would actually be going in the opposite direction of what I first thought. So one side of the wake would be what I have indicated in red below, and that side I can actually see in the picture (and I am fairly confident now that that’s the correct interpretation, judging from the shape of the feathery winglets). The green second part of the wake is just my guess of where it would have to be if my idea of where the ship is is correct.
Ship 2 (now shown in yellow) is still going the way I thought it was. Phew ;-)
But there is one part of the picture that I think is especially cool: The actual interference part where parallel wave crests seem to appear out of nowhere (crests marked in red below, troughs in blue). This is a possible mechanism for the creation of those parallel wave crests marked in blue above, too, but I don’t think that that’s what had happened there. But I am confident that that is what happened for those waves marked below.
Now it’s your turn, Elsa and Pierre. Do you remember what was going on? How well am I doing interpreting waves? ;-)
This is SO MUCH HARDER than seeing stuff in pictures I took myself and remember the situation! You poor guys always seeing my pictures without good explanations of what is going on on them. I think I might have learned my lesson here…
Last week, we ran an “expedition learning” course for 17-year olds. They were separated into several groups, working on different topics, and mine (unsurprisingly) worked on waves. You can see here what kind of stuff we observed when first testing the stretch of coastline we wanted to do our expedition to. And now you’ll get a picture dump of the actual expedition.
We started out in not-so-ideal-but-really-not-too-bad-either kind of weather, as you can read off the tracks below: It had been raining a little, but not very hard, and it had stopped by the time we got there.
The drift lines looked quite promising.
My group dove right into it (only figuratively, luckily, not literally). However I wasn’t quite sure if this guy knew what he was getting into?
At this point we were still very close to the car, so I thought that it might be quite smart strategically to let them figure out here how high the waders go and what happens if the waves are higher than the waders… And the wakes of two ships meeting up at a headland are a very good place to learn about that kind of things!
This headland is a very good place to start observing waves in any case. Especially at the typical wind direction found here. Because then, looking back from the light house to the land, you see a large area that is sheltered where waves only build up gradually. Which is a very nice contrast to the waves arriving upwind and makes it very easy to observe differences.
And then if you look downwind from the headland, you see waves sneaking around the headland from both sides. Those coming from the right are from the fully developed wave field that has been growing all the way down Kiel fjord, and then those coming in from the left are the ones that only started growing downwind of the little barrier shown in the picture above.
Can you see it? Maybe easier on a panorama kind of picture?
Of course we always like to look at the ring waves that appear when other waves hit stones…
I didn’t foresee that wave watching would happen mostly from within the water, but the guys in my group made a good case for walking on the sand bank to actually measure the wave hight depending on the water depth (rather than just observing and estimating from dry land, as I would have done), but why not?
Luckily, they found the shallowest part of the sand bank in exactly the same spot I would have told them to look for it based on the wave field ;-)
Btw, a nice example of coastal dynamics right below. We had a coastal dynamics group, too, but I don’t even know if they looked at this kind of stuff, I mainly saw them taking soil samples.
And I know I made the same observation in the same spot last time, too, but I think it’s fascinating how the different directions of the ripples and drift lines and waves all come together.
In any case, a nice day at the beach!
Well, most of the time anyway.
Luckily, we found shelter!
Those, btw, are Annika and Jeannine, who were working with a different group on coastal vegetation.
But: New and interesting pattern on the beach once the rain was done!
The kids spent the next two days putting all their observations on maps and preparing a presentation, and I am really happy with how it turned out. Of course there is some room for improvement still, but how boring would it be if there wasn’t? ;-) All in all I think it was a pretty successful course!
Of course I did not only take pictures of lighthouses and instructional activities during the teacher training at Lotseninsel last week. I also took TONS of pictures of water! Some of which I’ll share with you now.
For example below you see where the Schlei flows into the Baltic Sea. This is actually a fairly narrow outlet, and you can see the strong current and the eddies that are formed where it flows into the Baltic Sea! It had been raining a lot previously, so there was a lot of water trying to get out of the Schlei!
A similar pattern can be spotted at the outlet of the marina, but in this it’s mainly wind-driven.
And very nice here: Long swell and short wind waves on top of it.
Of course I also looked at wakes. This is a particularly nice one:
Oh, and reflections. Isn’t it super pretty how the mast gets reflected with all these little twists and turns?
And then we had some shielding from the wind, and waves only appearing after a certain fetch.
Btw, that’s the house we all — and all the teachers — stayed in.
Here we see waves being dampened by some algae stuff, and being deflected downwind of those patches.
Here is another view of the strong current going out of the Schlei and the distinct separation between the two water masses.
And now the same thing in combination with the sailboat’s wake. So pretty!
When we were on our way home, the wind had picked up substantially and we saw lots of foam stripes! Langmuir circulation, nowhere near the coast line.
Here we get a last glimpse of the house we had stayed in… And more foam stripes!
And some more ;-)
And then in Maasholm, we see the waves arriving upwind of the pier and then the tiny ones in the sheltered area. You can see a gust of wind somewhere in the foreground to the right, where there are all those small ripples in a darker patch.
It was a pretty windy day!
And more foam stripes…
And a wake!
And another wake!
And just a couple of pictures of water, because I love water.
I really like it when waves reach a sea wall at an angle, because the resulting criss-cross looks so cool :-)
And especially cool when you see it gradually building up, like below where the sea wall is partly protected by the gravel (or whatever you call those heaps of stones running in parallel to the sea wall?). The energy of waves hitting the sea wall at that part is dissipated, hence no reflected wave is sent off. However waves that hit the sea wall directly are reflected. Can you see how the reflections spread?
In July I will be involved in teaching an “expedition learning” course for a week. It will be all about coastal protection in the Kiel region, so two colleagues and I went on a private expedition to scout out what can be explored where. This is a very picture-heavy post, be warned! It’s more a note-to-self to document the different beaches we looked at than something I expect anyone else to be interested in.
We started out in Friedrichsort, where there were nice breaking waves to be observed. My part of the course, you might have guessed it, will be on observing waves…
In Friedrichsort there is a lighthouse on a small headland, and there are sand banks around it that make for very interesting wave fields, like for example below, where the sand bank almost seems to filter out some wavelengths.
Looking seaward over the sandbank, we see breaking waves over the shallow part, and waves being bent around the sand bank.
A similar thing could be seen on a tiny headland: Can you see how one and the same wave crest gets wrapped around the headland?
See? So cool!
Btw, you might have noticed the weather changing a lot over the last couple of pictures. It’s April, I guess… But a couple of raindrops here and there make nice tracers for the time since the last wave washing up over the beach ;-)
Always fascinating: When you can see wave-less spots that are shielded from the wind, and then local wind waves and others that are travelling in from further away. And breaking on a sand bank…
Also, did you see how nice the weather was for a couple of minutes every now and then? ;-)
And here is a close-up of the waves breaking on the sand bank.
Oh, and looking back to where we came from: That’s the lighthouse on it’s headland right there! And my two colleagues figuring out what’s wrong with the GPS they brought. Their part of the course will focus on more geological things than mine…
But I really like this view!
See how nice and regular the waves are that reach the beach even though the local wind field is really messy (as you see a little further offshore) and the waves have gone over the sandbank?
Oh, and always one of my favourites: When nice and regular waves hit a stone and it sends off wave rings. Love it!
One more, because it’s so nice!
And here waves bending around a wave breaker thingy.
And this is a picture that really nicely shows how if you don’t have wind, you don’t have waves. The lagoon there is sheltered so well that you can actually see the reflection of the bird sitting on the edge!
And here we have a very nice superposition of waves coming from different directions and with different wavelengths.
And waves coming through the “slit” between sandbanks and spreading as segments of a circle. Nice!
Oh, and more waves breaking on the sand bank.
After a while, we reached Falckenstein:
Not so far away from where we started out at that lighthouse over there:
Another interesting superposition of wave fields.
Oh, did I mention we did a lot of walking in the sand? About 20k steps. Well, I guess that isn’t even too bad…
Below I really liked the criss-crossing of waves. It’s actually one wave crest crossing itself after being bend by the shallowing water.
And those waves get deformed a lot, too!
And here we knew that it was a matter of minutes until those rain showers would be where we were…
Luckily, this shower went over quickly, too.
And this is the kind of stuff the other courses will be dealing with: Awesome formations in the coast!
Ha, another weather front:
And this is my favourite geological feature: there are interesting features in the sand/soil/stone (however you call it?) and then erosion marks, clearly made by water, right below!
A little bit further along the coast, there are weird wave breakers and if the wind hadn’t died down, we would probably have been able to see more interesting waves than these…
But the waves below were really cool: There were the ones that you clearly see on the picture at an angle to the coast, and then there were waves that came in perpendicular to the coast (so the wave crests were parallel to the coast) and they washed the other waves on the beach and back into the sea. I should really upload the movie…
So those waves above caused ripples in the sand which are parallel to the water line, even though in the pictures the other wave field is a lot more visible!
We ended up in Schilksee and had a look around the marina. Apart from the typical wind / no wind resulting in waves / no waves, we saw……
…this! Pretty cool, huh?
One last look at the coast near Bülk.
At this point, only one of us still felt like exploring every nook and cranny…
Even though there were some pretty nice wave fields, but we could see them from our vantage point without doing an extra step ;-)
Actually, there were a couple of cool features on the beach still. What’s up with those little bays?!
We ended the day with trying this very cool contraption to measure the coast with. It was actually a lot of fun!
And you wouldn’t believe how much work it was to hold that ruler thingy in the wind!
So yeah, that’s what we did. And how was your day in the office? :-)
I think I might need to find a new route to walk along the Kiel fjord. When I was walking — in the most beautiful sunshine! — with my friend over the weekend, she pointed out that there are funny waves and it looked like there was water dripping in, and I went without looking “no, there is a step right there that’s causing those“.
You see it in the picture below: Every wave crest washes over the step, and then when it retreats it sends off its own little waves.
It’s a funny thing with professionalized perception. What I notice walking along the Kiel fjord is really highly trained and specialised, I guess. But still a lot of fun! And it makes me really look forward to the excursion that I’ll do later this summer with a couple of high school students where they’ll learn to observe waves my way :-)
What’s discussed in that article is that while many wave interactions can be seen as (more or less) linear, sometimes there are nonlinear effects that can be replicated in a model. So far so not surprising. But I got fascinated because the phenomenon they look at I have seen over and over again and never really paid any attention to it: Wave crests forming X or Y shapes. But looking through my archives, I even had dozens of pictures of this exact phenomenon! (Actually, I didn’t have to look further back than to a beautiful day last November, when I also observed the wavelength dependency of wave-object interactions)
Take for example the picture below: Do you see the H shape in the waves closest to shore? (In the article they would probably call it a more-complex shape, since it’s a double Y shape…)
Below I’ve drawn into the picture what I mean by H-shape in green, and the typical kind of linear wave interaction in red (all crests just move on without influencing each other except in the spot where they occur at the same time, there they just add to each other):
Or below, I spot an X-shape:
And here are several X- and Y-shapes
And the picture below just to give you an orientation of where you are: Yep, it’s the same spot where we usually observe foam stripes, funny waves, or ice…
— Mark J. Ablowitz, & Douglas E. Baldwin (2012). Nonlinear shallow ocean wave soliton interactions on flat beaches Physical Review E, vol. 86(3), pp. 036305 (2012) arXiv: 1208.2904v1
All you regular readers of my book and my blog surely recognize what’s going on below?
Yes! A wave field comes in at an angle to the pier and gets reflected, leading to a chequered pattern. And a second wave field comes in with wave crests pretty much parallel to the pier, adding a little more interest to the pattern.
I love watching these kinds of waves! But it is really difficult to take good pictures. Sorry about the over-exposed background…