See the Music

You need to a flashplayer enabled browser to view this YouTube video

Cool effect. Since this is not slow-motion, you might think it has to be basic aliasing: seeing a beat between the oscillations of the string and the frame-rate of a camera, often seen with wheels that look to be spinning slowly — or backward — on film. It’s not unlike the effect of a strobe light* that’s near the frequency of oscillation that make the motion seem slow or nonexistent, which sometimes happens with fluorescent (or rectified LED) lighting.

But it probably isn’t, or at least not in a simple way. When you strum a guitar the oscillations have a much longer wavelength. The fundamental mode is a standing wave where the string makes a half -wave (e.g. a 1m string has a wavelength of 2m), and there two nodes, one at either end. The next mode would have a node in the center and be a full wavelength. If the speed of sound is around 400 m/s, that gives a frequency of 200 Hz, or 400 Hz for the 2nd order mode. That’s about what we are hearing. The wavelengths shown in the video are much shorter, by more than an order of magnitude, and perhaps two. 20,000 Hz is way off. Plus the waveforms — you could get them by adding Fourier components, but that’s not going on here. This is a shutter effect, so it’s related to aliasing, but the sampling is happening as the exposure is scanned, i.e. each exposure is taking some time, and the exposure on the left side of the image does not represent the same time as the exposure on the right. This is called a rolling shutter and can have some pretty neat effects.

*Just bought a strobe. So I’ll be playing around with it.

2 thoughts on “See the Music

  1. The camera is rotated 90 degrees so that the rolling shutter direction is parallel to the guitar strings (examine the aspect ratio of the video). If the video frame rate is 30 Hz then a string vibrating at 300 Hz will show 300 / 30 = 10 wavelengths in one frame time. In a rolling shutter sensor, all of the pixels in a line are exposed simultaneously so there is no difference in sampling time of the leftmost and rightmost pixels in a line.

  2. Slight correction: the speed of sound is not the relevant speed in this case. It’s the speed of propagation of a transverse wave of the string, which is related to the mass/length and tension of each string…not the speed of sound. Anyway, as you suggested, the wavelength doesn’t matter in this case. You’re seeing the frequency.

    Otherwise, you couldn’t tune a guitar.

Comments are closed.