Strobe Lights and Guitar Strings (And Nodes)

Notes and Credits

The music in the background of the video includes "Lonesound," "The Wet Moist," "Mist Engine," and "Garbage Worms" by James Primate and Lydia Esrig.

Transcript

Today we’re going to be looking at the relationship between the frequency of a moving string and the frequency of a strobe light, how they can work together to produce very cool effects, how those effects actually work, and what we can learn from them.

A stroboscope like this one is capable of high frequency light emissions. With this dial you can adjust the flashes per minute, which can easily be converted into hertz. As you increase the frequency of flashes, it becomes more and more difficult to make out the intervals between them, and the light will begin to produce a more constant tone. As a matter of fact, the tone produced by the strobe light itself will actually match the frequency of the flashes. You can just look on the dial at the flashes per minute and multiply by 60 to figure out exactly what frequency - in Hertz - you’re hearing.

In a dark room, when the strobe light hits a moving object, you will essentially only see that object in snapshots occurring at the frequency you’ve chosen. Setting the strobe to 600 flashes per minute is kind of like watching a powerpoint presentation at 10 slides per second. By the way, you’ll have to excuse the darker parts of the video. They’re created by an effect on most cameras called rolling shutter, but that’s a whole other can of worms.

When viewing a moving guitar string, it appears to blur, because our eyes cannot properly track each step of its pattern of motion.

When shining the stroboscope on a moving guitar string, you’ll still see a blur at most high frequencies. That is, until you adjust the frequency of the light to match the fundamental frequency of the string. This’ll also work at divisions of the fundamental frequency. At this point, the string will appear to stay still, mostly. You’ll notice it isn’t perfectly still at first. This is because as the string is plucked, it will initially oscillate at a slightly higher frequency. This is due to the fact that we are slightly stretching the string by plucking it, briefly increasing the tension. This is the same principle that allows a guitar player to bend a string. When a guitarist bends a string on a guitar, they apply a force perpendicular to the string's length, causing it to stretch and increase in tension. This increases the frequency of the string's vibration, producing a temporarily higher frequency.

Why? Well, since the flash is occurring at the same speed as the oscillation of the string (or a division of the oscillation) we effectively only witness a snapshot of the same point of the string’s pattern of motion over and over (and over) again. Everything else takes place when the light is off.

In this graph, the waveform represents the motion of the string, complete with nodes and antinodes, the points of least and most amplitude respectively. The bulbs represent the timing of the flashes of the strobe. As both events occur at the same frequency, you can see how, no matter at what point the light begins to flash, all subsequent flashes happen at the same point in the repeating pattern of motion of the string. Pretty cool.

Like we said, doing this - matching the frequencies of strobe and string - results in the string appearing still. If we set the strobe frequency to be slightly off from the string frequency, we will see motion. You can see in this animation that a series of flashes, when slightly off, will each occur at different points along the oscillation pattern of the string.

When seeing this on a string, you’re not actually seeing the string’s complete motion, just an illusion made from subsequent points of that motion on completely different oscillations.

But there’s more we can do with this. Before, the string was oscillating at its fundamental frequency. If we lightly prevent the string from oscillating halfway up the string with our finger, we can create a point at which the string does not oscillate. This is a node of the string, a point of constant, zero amplitude. Two others are found at each end of the string, where they connect to the instrument. Creating a node causes the string to vibrate in two distinct parts, separated by the node itself in the middle. When seen during the flashing of the strobe, we can see the node clearly, and the separate vibrations on either side.

Here, we play the second harmonic of the string; by lightly pressing at a point one-third down the string we can see two nodes, and three separately vibrating areas between each. It is important to note that the frequencies of each separate area are multiples of the fundamental frequency of the string, so we don’t have to change the frequency of the strobe to see the illusion of the still string.

But why not? Sure, if the frequency of the guitar string is twice as fast as the frequency of the flashes, then there will be twice the amount of motion between flashes. Yet, as you can see here, the flashes still line up with the same points of that motion. Even increasing the frequency of the string to three times the frequency of the flashes, we see that the string remains visible only at the exact same point as before. Therefore, as long as the string’s frequency is a multiple of the strobe frequency, the illusion remains.

However, if the strobe’s frequency is a multiple of the string’s frequency, our careful trick will be broken. This graph shows two flashes every oscillation, one happening at the peak of the wave, the other at the trough. Seeing this in action looks blurry, because your eyes see the trough and the peak at the same time.

What's more, we can theoretically add as many nodes as we want by lightly pressing at specific fractions of the string’s length as we pluck the string. This process is somewhat complicated. Strap in. The first place a node can exist, as explained, is at halfway down the string. The next are at one-third and two-thirds down the string, and both of these will sound the same. It’s important to note that, as of yet, all of these fractions are unique, in that they cannot be simplified. This changes with the next set.

The next nodes are at one-fourth and three-fourths down the string. These sound the same as each other, and can’t be simplified either. In fact, they sound the same because they cannot be simplified. It’s only because two-fourths can be simplified that its tone will be different. two-fourths is just one half, like our first node, and it’ll still, of course, sound just like our one half node did.

Lets take it to the guitar...

All nodes created on a string will sound like the simplest forms of their fractional location on the string. Two-sixths sounds like one-third and, by proxy, two-thirds. Two-eighths sounds like one-fourth and, likewise, three-fourths.

Essentially, what we’re able to do with this strobe light experiment is visualise the node and antinode process right there on the actual string of the guitar, which would normally be impossible for the human eye, and all because we are actually seeing less than we would normally see under a typical, constant light source. Maybe it’s true that sometimes, less is more.