"This is What Happens When You Run Water Through a 24hz Sine Wave"
I'm not sure this is the best title. "What happens when you wiggle a hose at a frequency close to a camera's frame rate and then film the water coming out of it" might be better.
At the most basic level, this is just the game you used to play with a hose when you were a kid by waving the end and producing ribbons of water in the air. The video just added a camera trick to photograph the ribbon in the same place during each oscillation appearing to freeze it in place.
Initially I thought this was going to be much cooler, actually using the speaker to move the air through which the water was travelling to produce an effect. I was hoping for an awesome standing wave demo or something.
"The video just added a camera trick to photograph the ribbon in the same place during each oscillation appearing to freeze it in place."
This is such a concise summary and I'm totally with you. I think. If I understand right, it would not be impressive to watch in real life and is just a property of the recording. Correct?
It's important to remember the water does NOT actually move in a wiggle like that.
Obviously it's impossible for water to change directions like that without something pushing it.
Instead the end of the hose is shaking, causing some water to flow on the left of the screen, and some on the right.
The water moves straight down! But it's in bursts.
But if you time the camera right you catch the bursts always in the same place, and it looks like a zigzag.
Imagine a piece of paper being pulled, and a pen wiggling back and forth. The paper (i.e. the water) moves exactly straight. But the motion of the pen (i.e. the hose) makes it look like a zigzag, but each portion of the paper only moves straight.
It seems like it would be much cooler with the strobe, as it's easy to change it to any frequency along with the speaker frequency (compared to dynamically changing the frame rate on a camera [though, that sounds awesome]). I also wonder what the stream looks like in real life, but am amused that I cannot trust any video to show me.
A video taken at 48 frames/sec or more would begin to show you the "truth". The faster the frame rate, the more true to life it would become. This is a perfect example of a signal approaching the Nyquist frequency of the system sampling it.
With a camera of exactly 48fps and a wave of exactly 24hz you would see two intertwined jets. (It would be nice to see it. An easier implementation it is to use a 24fps camera and a 12hz wave.)
With 48fps you can reconstruct any signal whose frequencies are less than 24hz (for example sin(2pit/23)+1/2 sin(2pit/17)). But the reconstruction algorithm must be implemented in a computer.
The eye/brain simply "join" the nearest images of consecutive frames, so video with a 23hz signal sampled at 48fps would looks like two intertwined jets spinning slowly upwards. A computer algorithm (or a looot of hand calculations) can reconstruct the real only one jet falling down.
Eyes don't work like that at all. They're continuous. You can fake motion with a low rate of pre-blurred frames, but parts of perception can get all the way up to hundreds of fps.
I was hoping for a standing wave too. One of the most fun things we did in physics class last semester was attach an oscillator to a tense string and try to find the tensions that would produce a nice standing wave. It's really trippy to watch a string rise up into a stable wave right before your eyes, no frame-rate tricks required.
The naked eye is subject to persistence of vision but if you wanted to see strobe effects in person either a strobe light or spinning wheel with view gaps could be used.
Actually, the human visual system has a particular image repetition frequency, above which we interpret the input as continuous. This is called the flicker fusion threshold:
Now one may ask -- how do movies, running at 24 frames per second, appear to be continuous, since 24 Hz is below the FFT? The answer is that a movie projector splits each 24 Hz frame into two frames with a moving shutter, resulting in an apparent frame rate of 48 Hz, high enough to appear continuous.
I am familiar with flicker fusion, and many of the theories that account for it, as well as Purkyně's pionering work in these matters. But my sense of it is that it is a neurological phenomenon, the brain and the eye working together (happy to be corrected, though).
So I still conclude that light falls continunously on the retina, and is continuously processed. But, I will further nuance this, by stating that, in the very contrived and special circumstance of very similar images in sequence, representing motion, appearing in rapid progression at a certain controlled rate, are spontaneously perceived as motion (an illusion) by the brain and the eye working together to make sense of a visual phenomenon that does not exist in nature, but only under artificial circumstances.
> But my sense of it is that it is a neurological phenomenon, the brain and the eye working together ...
Yes, that's correct -- it's both.
> So I still conclude that light falls continunously on the retina, and is continuously processed.
Yes, unless it's periodically interrupted, as with a flashing source. In that case, it's a discontinuous flow of visual information that we must assemble into something meaningful.
> to make sense of a visual phenomenon that does not exist in nature, but only under artificial circumstances.
People are wired by natural selection to fuse a discontinuous series of images into an apparent continuous sequence on the ground that this makes us more fit to survive -- so it does exist in nature, it's not artificial.
Consider a primitive man, or one of humanity's predecessors in the long history of evolution, watching a prey animal running through a forest. Our distant relative sees the prey animal between two closely spaced trees at one moment, then sees him between two other trees a bit later. With this limited information, he is able to infer (a) the prey's speed, and (b) where he will be five seconds from now, where he intends to be. This is all based on our ability to ... wait for it ... fuse many discontinuous images together.
Unfortunately no, our eyes don't have a simple "refresh rate." Instead, you'd have to control the light to arrive at the eye at the right frequency - which you've likely experienced through strobe lighting.
Petapixel[0] has a better explanation. It is an illusion created by the synchronized frame rate and oscillation. They have used the same trick with a strobe light for live effects.
I bet this would work much better with glycerin or glycerin/water mixtures. Water has a low viscosity, meaning it's relatively easy to induce turbulence. And turbulence, while not exactly chaotic, is somewhat random and nonperiodic.
I feel like there's some information theoretic approach which could be leveraged here, and maybe in similar systems - ie. just from the video we can work out
- The difference in video frame rate vs sound frequency based on the period of the wave
- Maybe the structure of the wave itself based on the waveform, although maybe not.
Wait, if I'm interpreting the Shannon-Nyquist theorem properly here, doesn't that mean since the signal is 24 Hz that we'd want a 48 FPS frame rate to accurately get the signal?
But in this case they don't want that. They want the illusion that the water is standing still, which you get by sampling the signal at the exact same point in every cycle. So to the sampler/viewer it looks like there is no signal at all.
Kind of. From the description in the YouTube video:
Set up your camera and switch it to 24 fps. The higher the shutter speed the better the results. But also keep in the mind that the higher your shutter speed, the more light you need.
Motion blur isn't something you "turn off" -- it's the natural effect of light being collected over time. The faster the shutter speed, the less time the camera spends collecting light each frame. That means both less motion blur and a darker image.
I'm not sure this is the best title. "What happens when you wiggle a hose at a frequency close to a camera's frame rate and then film the water coming out of it" might be better.
At the most basic level, this is just the game you used to play with a hose when you were a kid by waving the end and producing ribbons of water in the air. The video just added a camera trick to photograph the ribbon in the same place during each oscillation appearing to freeze it in place.
Initially I thought this was going to be much cooler, actually using the speaker to move the air through which the water was travelling to produce an effect. I was hoping for an awesome standing wave demo or something.