Guitar oscillations? How do they look?

[mahrap]

So I recently came across this video in youtube: . The vibrations of the string definitely look like sinusoidal waves to me and I know that if a string is fixed at both ends then it will display the pattern of nodes and antinodes by producing a standing wave at certain frequencies. Is this how the guitar strings vibrate if you played the right harmonics?

 

[Jano L.]

The little waves that appear on the strings are probably a stroboscopic effect of the camera due to finite scan frequency. You can see similar waves if you look the vibrating string in front of the CRT monitor picture (the picture blinks with freq ~ 60 Hz). The strings themselves actually do not have such shape, their shape is mainly due to oscillations of the first harmonic, whose wavelength is twice the length of the string.

 

[bahamagreen]

The apparent amplitudes are correct, but the apparent wavelengths are too small - it is an artifact of the scanning frequency of the camera. For example, the frequency of the open low E string (the top string in the video) is about 80 Hz. The length from nut to saddle is about 25 inches. The string goes back and forth to make one full wave, so twice 25 inches would be the wavelength... 50 inches.

So the wave is moving through the string 50 inches... 80 times per second.
This is a metal core string with a fine wire metal winding around it under about 20-25 lbs of tension when tuned to pitch.
80/s x 50in = 4000in per second
= 333 ft/s
= 227 mph

That is much faster than the camera scan rate can resolve, and that is the slowest of the guitar strings.

 

[A.T.]

Check out:

https://www.youtube.com/watch?v=6sgI7S_G-XI

And this at 6:00 :

https://www.youtube.com/watch?v=QXjdGBZQvLc

The effect you see in the IPhone camera is a capture artifact, as others said:

https://www.youtube.com/watch?v=O8vBPr36YUo

 

[sophiecentaur]

The apparent amplitudes are correct, but the apparent wavelengths are too small - it is an artifact of the scanning frequency of the camera. For example, the frequency of the open low E string (the top string in the video) is about 80 Hz. The length from nut to saddle is about 25 inches. The string goes back and forth to make one full wave, so twice 25 inches would be the wavelength... 50 inches.

So the wave is moving through the string 50 inches... 80 times per second.
This is a metal core string with a fine wire metal winding around it under about 20-25 lbs of tension when tuned to pitch.
80/s x 50in = 4000in per second
= 333 ft/s
= 227 mph

That is much faster than the camera scan rate can resolve, and that is the slowest of the guitar strings.

The posh term for this is Temporal Sub-sampling. It's the same basic effect that you get when car and wagon wheels appear to be going at odd speeds and even backwards. The string is vibrating at hundreds of times a second but the camera is taking pictures at 24 per second; this gives 'alias' artefacts because the recorded images miss out information about what's happening between frames. Moreover, each frame is probably being scanned from side to side during the 1/24s interval. I wouldn't mind betting that you'd get a different portrayal of the waves on the strings if you rotated the iphone by 90 or 180 degrees.

It's very pretty though!

 

[rcgldr]

This was the best I could find for relatively high speed capture of a relatively slow moving string:

bse_string.mov

I recall some high speed cameras (1000 to 1,000,000 frames per second) being used to capture stuff, but couldn't find one of a vibrating string.

 

[sophiecentaur]

That's good!