Guitarmonic Oscillators

You are seeing a demonstration of the Nyquist Shannon theory on aliasing.

It's very simple and so is the math.

The frame rate of the video is essentially how fast the image is sampled (sample rate). Think of it as a digital recording or even a still camera that is taking successive pictures at a specific period or rate

The vibration of the strings also have a specific period.

When you combine the two rates you find it works almost like a strobe light. If its flash rate is the same as the oscillating string the string appears frozen at some point in its oscillation.

Change the frequency of the strobe slightly and the string appears to vibrate at a very slow rate. As the two frequencies get further apart (flash rate versus string oscillation frequency) you see the string take on patterns as you do in the video.

You can do the math yourself as frame rate is in frames per second and the string oscillations are also cycles per second (Hertz is the modern term).

When the two are different you get what is called beat frequencies.

I'll bet it's even cooler when you're stoned.

isn't everything?

What is interesting but not surprising to see is how far the strings actually move.

Bass strings yield a good bit of displacement and you can see them when you play, but I suspect the player is laying into those strings a bit.

When striking hard on the top E string of my (right hand) guitar, it will go sharp initially because the "wave" is geometrically needing more length, thereby putting more tension on the string. It's even more pronounced when going to a drop-D tuning.

The same effect is what makes wheels (on TV and in movies) sometimes look like they are spinning backwards when the vehicle is moving forward.

Back when 'westerns' were popular on TV, it was common to see stage coach wheels appear to be spinning in reverse. As the stage coach slowed down the speed of the spin would change and sometimes the wheels would appear to spin forward, backward, then forward again.

Actually, what we might be seeing in that video may be the product of what is called a rolling shutter.

It depends on what was used for the camera in the link, but some use a shutter that is a slit that slides before the sensor.

Rolling shutters are notorious for making propellers look bent as well as providing a stroboscopic effect.

Some of the strings took on almost a square wave or distorted sine wave look instead of a smooth sine wave.

An experiment with opto-electronics using a guitar turns out to be interesting. Something to goof around with.

In the interest of clarification, I meant modulating a light beam with a guitar string. It works. I have not tried it with lasers.

Couple more idle observations. Go back and play it again, and keep starting and stopping it. Although when played continuously, the waves look like simple sine waves, when you look at freeze frames, there are some interesting wave forms that your eye/vision processing isn't fast enough to resolve. Lot going on there.

I wouldn't have expected a cheap phone camera to have that much depth of field, where the strings at ~10cm and the clouds at infinity are both in focus. Or maybe it's because it's a cheap phone camera.

jhammond

That's why I think it is a rolling shutter video camera.

That is exactly what I would expect to see from a rolling shutter.

Yes but. The player puts the camera into the aperture beside the strings. There is just about enough room to manoeuvre a phone or flat compact camera, but there is absolutely no room for a video camera with a rolling shutter. However, the camera sensor has to be scanned, which may provide the same effect.

AH, your correct. Most if not all CMOS digital cameras use rolling shutter in digital form either horizontal or vertical scan of the sensor. So it the image moves in time of the scan you will see the change. That's why props look bent, guitar strings show waves.

Google rolling shutter camera

https://www.google.com/search?q=rolling+shutter+camera

Here is an interesting article on the effects of rolling shutters...

http://www.diyphotography.net/everything-you-wanted-to-know-about-rolling-shutter/

We used to have oscilloscopes plugged into the stereo so we could watch the wave patterns of different musical instruments.

One time I watched the backside of this double bass travel about an inch when it was being played to it's fullest. About the same as a subwoofer.

Using an LED Flashlight, (but one which is dim-able via pulsed modulation), will give some fascinating results when used as a small strobe light. In darked areas, shine it on any moving or ocsillating object to get the effect as shone in the video. Spraying water from a garden hose illuminated thusly will give lace-like patterns.

Years ago I would tune my guitar against a detuned TV screen. If low the wave would travel in one direction and if high it would go the opposite way. When spot on the wave would be a standing wave. Of course this may depend on the screen refresh rate but for the standing wave it seemed to work well.