Guitar String Oscillations!

This intrepid guitarist put an iPhone inside his acoustic guitar to capture the string oscillations with amazing results. Below, I'll explain a little about what's happening, and also dig into some of the physical aspects of sound creation on the guitar.

Pretty cool, right?

What's happening in the video is the result of an effect called rolling shutter. Basically, the sensor in the iPhone doesn't capture each frame of the video instantaneously, but rather scans in a "right to left" pattern. The strings are moving faster than the camera's image sensor can scan, so different sections of each string are captured at different points in motion, resulting in a waveform shape. (Whew! Still with me?)

While the waveforms in the video don't exactly represent what we might see on an oscilloscope, they do create an opportunity for us to explore some fundamental aspects of sound production. First, a few definitions:

1. Frequency - The rate at which a vibration occurs that constitutes a wave, either in a material (as in sound waves), or in an electromagnetic field (as in radio waves and light), usually measured per second (Hz).
2. Amplitude - The maximum extent of a vibration or oscillation, measured from the position of equilibrium

In the video above, each string takes on a particular moving shape after being plucked. The shape (sequences of alternating hills and valleys) can be seen as a representation of both frequency and amplitude. Frequency is represented by the number of times a particular hill/valley pair appears on a string, and amplitude by the size of the hill valley pair.

Lower pitches have a lower frequency (rate of hill/valley repeat), while higher pitches have a greater frequency, and these rates of repeat are measured in cycles per second, or Hertz (Hz). On a guitar in standard EADGBE tuning, the strings vibrate at the following frequencies:

• Low E: 82.41 Hz
• A: 110.00 Hz
• D: 146.83 Hz
• G: 196.00 Hz
• B: 246.94 Hz
• High E: 329.63 Hz

This means that when you play the high E string open, it completes 329.63 hill/valley pairs every second! Pretty cool.

In the video, you can see frequency in the spacing bewteen the hills. Lower pitched notes, vibrating at lower frequencies, have lots of space between the peak of each hill. Higher pitched notes have very little space, and look much 'pointier' as a result.

The frequency of octaves has an interesting mathematical relationship. To get to the next highest octave, you simply double the frequency of your starting note. In the list above you'll see that the Low E string vibrates at a frequency of 82.41 Hz. To get to the next octave (ex. fret 12 on the low E), we'll double the frequency to 164.82. What happens if we double that number again? We get 329.63, the vibrating frequency of the High E!

If you skip to 2:02 in the video you can see the frequency difference quite clearly. First, the guitarist strums each string open, then plays each as a 12th fret harmonic (which is one octave higher than each open string). The harmonics have a visibly faster rate of motion, while retaining a similar shape to the open string.

[Sidenote: To play a harmonic, place your left hand index finger on a string, directly over the 12th fret. Don't push down, just touch the string lightly. Now pluck the string with your pick and you should hear a clear bell-like note one octave higher than the open string.]

Okay, so we have this whole frequency thing figured out, but what about amplitude? In the video, amplitude can be seen as the size of the hills/valleys. When the guitarist first strikes a string the hills are large, gradually decreasing in size as the note fades out. As you might already be guessing, amplitude is the volume of a sound. The taller the hills the louder a particular note sounds to us, and vice-versa. Combine this with frequency, and you get something like the shapes in the video.

So that's it! With a simple but ingenious YouTube video as our guide, and a little know-how, we've (either totally blown up our brains or) gained greater insight into what happens when we play the guitar. If you'd like to learn more about how physics applies to the guitar, keep an eye out for future blog posts!

Good luck, and happy shredding!

ck

Chris Kuklis teaches guitar and all sorts of fun stuff. To learn more about the science behind sound, check out Chris's BML page and schedule a lesson.