Tag Archives: interference

Intriguing interference pattern of waves

Do you see those weird traces going away from us, perpendicular to the wave crests, but in parallel to the bright stripes on the sea floor (I talked about those in yesterday’s post), looking almost like waves but not quite? What’s going on there?

Something very cool! :-)

In the gif below, I have drawn in several things. First, in red, the “weird” tracks that we are trying to explain. Then, in green, the crests of two different wave fields that are at a slight angle to each other. I’m first showing one, then the other, then both together. Lastly, I am overlaying the red “tracks”.

So this is what those tracks are: They are the regions where one of the wave fields has a crest and the second one has a trough (i.e. where we are right in the middle between two consecutive crests). What’s happening is destructive interference: The wave crest from one field is canceled out exactly by the wave trough of the other field, so the sea level is in its neutral position. And the wave fields move in such a way that the sea level stays in a neutral position along these lines over time, which looks really cool:

Some more pics, just because they are pretty and I like how they also show total internal reflection :-)

And don’t you just love the play of light on the sea floor?

And even though these weird neutral sea level stripes are parallel to the bright stripes on the sea floor, I don’t think that the latter one is caused by the first. Or are they? Wave lengths seem very different to me, but on the other hand what are those stripes on the sea floor if they aren’t related to the neutral stripes in the surface??? Help me out here! :-)

Wave watching by proxy — looking at how waves focus light on the sea floor

What is it that we actually look at when we go wave watching? Water is pretty much clear (or at least it is in the spots where I like to go wave watching), so how come we are able to see waves?

What we are looking at are not actually the waves themselves, but at how surfaces oriented in different directions reflect light from different directions towards us, and usually the light isn’t uniformly distributed, so we see lighter and darker areas on the waves that are associated with certain orientations of the surface, i.e. the slopes going up and down to and from the crests.

But this only happens if we look at water at a small angle — then the water surface acts to reflect most of the light from above. However if we look at water at a steep angle, we are actually able to look inside. See this in the picture above? This is due to a phenomenon called total internal reflection.

Now that light easily gets in and out of the water, the water surface does something weird: It acts as a lens and focusses light on the sea floor so we see bright areas and not so bright areas. And looking at how the brightness is distributed on the sea floor, we can figure out what the waves must be to have focussed the light in exactly that way, even though we can’t see the water surface.

Let’s start with an easy example. Below, you see the half circles of concentric waves radiating away from some obstacle at the bottom of the sea wall. The further away from the center you look, the more other waves you notice as the concentric circles become more and more difficult to see.

Moving on to a slightly more difficult case below.

You see the waves radiating away from the seagulls. Behind them, at a shallow angle, you mainly see the ambient light of the sky reflected on the waters surface to let you see the waves. Towards us, though, at a steeper angle, it gets more and more difficult to see the water surface and the waves, but we start seeing the light focussed on the sea floor, mirroring the circles of the waves above.

Here is another example of waves , except this time we see because of reflection of light on the surface further out, vs focussing of light on the sea floor closer to us, except that this time we are not looking at the same waves any more. The waves further out are wind waves and waves the birds made, the waves further in are similar to the ones in the second picture — created by an obstacle at the base of the sea wall.

But then sometimes it gets really difficult to reconcile the waves we see through these two different phenomena. Below, the wave field we see by looking at the light reflected at the surface seems to be dominated by wave crests coming towards us, with the crests being more or less parallel to the sea wall at the bottom of the picture. There is some small stuff going on on top of that, but it doesn’t seem very important.

But now looking at the pattern of light on the sea floor, we pick out something very different: The dominant wave crests are now perpendicular to the sea wall when you look at the middle of the picture below (towards the bottom we see those half circles again that we saw above, too)! Where do those wave crests come from that are perpendicular to the sea wall?

There are actually two things I can think of.

First: they are actually an important part of the wave field, we just don’t pick them up very well because — in contrast to the waves coming towards us with the side going up towards the crest reflecting the dark land behind us and the side going down towards the trough reflecting the bright sky — waves going perpendicularly to that field would mainly reflect the sky, so it would be hard to make out their crests and troughs since they appear to be the same color.

Second: I’m not actually sure this makes sense any more. I was going to say that the surface shape of wave crests moving away from the sun might be more suited to focus light than wave crests moving in a perpendicular direction. But looking at all the examples of circular waves that I posted above and that show up as circles, not just in areas where the wave crest was in specific directions, this probably doesn’t make sense. If anyone is reading this, what do you think??

Below is another example: Here we see a crisscross of waves, a checkerboard pattern of an incoming wave field and its reflection — as long as we look far out onto Kiel fjord. If we look into the water at a steep angle, we see again wave crests that don’t seem to match what we saw on the surface! (btw, don’t let yourself be distracted by the ripples in the sand that might look like they are also caused by light being focussed by the water surface. They are just ripples in the sand…)

Clearly I need to think about this some more to figure out what’s going on here. I’m grateful for any input anyone might have!

Forget about big waves, today we are focussing on the details!

Today we are focussing on tiny waves right near the shore inside the sheltered harbor. See how below there are two wave fields, one with longer waves with crests that are parallel to the water’s edge, and then shorter ones propagating at a right angle relative to the first field?

Where the rope swims on the water you see how the short wind waves are stopped and only start forming again at a distance downwind of the rope.

The same here: Where there are ropes floating on the water, the water’s surface looks a lot smoother because the wind waves that propagate perpendicularly to the ropes are erased. But there are some wave crests parallel to the rope, formed by the rope hitting the surface and being pulled out again!

Below, the ropes don’t actually touch the water’s surface, but we have cool reflections of waves with crests parallel to the two walls that form the corner. The water level is right at the height where there is a little ledge on the wall that gets flooded with wave crests arriving and then falls dry during wave troughs. This causes this cool pattern of wave crests that seem to be interweaved right at the corner.

Sometimes looking really closely at small scale pattern is even more fun than looking at the sea and all the big and flashy (or splashy?) stuff going on there!

Ferry sailed past, wake perpendicular to wind. Cool interference pattern!

Guess the title says it all today ;-)

Just kidding. Below you see a movie of a neat interference pattern I observed this morning. The situation is similar to yesterday in that the ferry has sailed past and the wake runs up on those bathing steps. But: today it’s quite windy and the wind waves’ crests are perpendicular to the crests of the ferry’s wake. Check it out:

That’s the kind of stuff I loooove watching! Happy New Year, everybody, may there be plenty of wave watching in 2019!

P.S.: Am I the only one who always wants to write fairy when writing about ferries? :-D

Experiment: Interference of waves

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).

Screen shot 2015-08-16 at 11.44.47 AM

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.

Awesome interference pattern in a Norwegian fjord

“Hei Mirjam.

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.”

Wow! Thanks, Pierre! :-)

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…

Expedition learning

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!

Weekend wave-watching

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.






Waves reflecting on a sea wall

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?

See it more easily in the movie below: