One of my violin instructors once told me that there were tiny hairs all over the violin bow that each grabbed the string and plucked it, and that this series of plucking is what we actually hear when someone bows a string. He played his violin gorgeously under this assumption despite the fact that it was irredeemably false.

             The violin is an intricate machine that goes through a complex process to produce its sound. This process begins with the interaction between the bow and the strings. Violin strings were originally made of animal gut, but most modern strings are made of metals such as aluminum, steel, and sterling silver. The violin has four strings tuned to the notes E, A, D, and G (from highest to lowest frequency). For reference, the G here is the one just below middle C on the piano.

Most bows are made of horse hair and rubbed with rosin (essentially solidified tree sap). The rosin keeps the coefficient of static friction between the bow and string high, while keeping the coefficient of kinetic friction relatively low. In simpler terms, it is hard for the string to become unstuck from the bow, but not hard for the string to slip and slide on the bow once it is unstuck.

This relationship produces a phenomenon called the “slip-stick” effect which is illustrated here (animation by Heidi Hereth). As the bow is drawn across a string, the string sticks to it and is pulled along with it. At some critical point, the force of the bow overcomes the static friction force that kept the string stuck to the bow, and the string is released. It slides all the way down to a point where it is picked up again, and the process repeats. This cycle occurs hundreds of times per second when playing a note on the violin. It is this pattern of tension and release caused by the bow that is “felt” by the bridge, the wooden piece that holds up the strings and connects them to the belly of the violin. The bridge vibrates, transferring this information to the rest of the body and eventually to your ears.

The pitch of the note you hear depends directly on the fundamental frequency at which the string vibrates. Frequency, when in the context of waves, is the number of full cycles that occur in a certain amount of time. This frequency is affected by the string’s tension, which is controlled by tuning the strings with the pegs that stretch or release the string. As the tension increases, the frequency increases. Even if you don’t have a violin handy, you can still hear this effect when plucking a rubber band stretched to different tensions.

The density of the string (the mass per unit length) is also a factor in the frequency of vibration. The lower three strings, A, D, and G, generally have a metal wire core and are wound in additional wire. This additional wiring increases the density of the string without affecting the tension. Higher mass per length causes the string to move more slowly, and therefore to vibrate at a lower frequency. Finally, the length of the vibrating string affects the frequency. When a violinist presses the string down to the fingerboard, she decreases the length of the part of the string that is free to vibrate, increasing the frequency as a result.

The fundamental frequency is the lowest frequency at which a certain string can vibrate. The violin string can also vibrate at harmonic frequencies, integer multiples of the fundamental. Generally speaking, the string will vibrate as a composite wave of the fundamental and many of its harmonics. The speed, pressure, and placement of the bow all have effects on the harmonic overtones of the produced sound. The combination of the fundamental and harmonic frequencies allows us to distinguish the sound of a violin from other instruments that make sound at the same fundamental frequencies. The harmonic makeup of the violin’s sounds characterizes its smooth and wilting timbre in contrast to, say, the brighter and raspier trumpet.

 

me-and-lucia
Me as a whipper snapper violinist in Italy. Mrs. Lucia was not messing around.

One interesting feature of the violin is that certain harmonic frequencies can be isolated from the fundamental and the lower harmonic frequencies and played by themselves. There are certain points on a bounded vibrating string called “nodes” where the string does not move, but either side of it is oscillating back and forth. Certain harmonics have nodes at specific places on the string, namely rational fractions of the total length. By placing a finger lightly (so as not to dampen the lower part of the string from vibrating at all) in one of these places, the string is forced to vibrate at a frequency that has a node in that place and where the string around it oscillates. Due to the geometry of these nodes and their corresponding harmonic frequencies, any harmonic lower than the one with a node in that specific place, including the fundamental, is unable to show up in the total makeup of the sound. The result is a light, high end whistle.

Even more complex and interesting physics happens between the time the vibrations reach the bridge and the time the sound waves reach your ears, but that is for another post. We have enough information now to prove my well-intentioned instructor wrong.

Violin strings vibrating by themselves make little to no sound. They must be attached to the body through the bridge for the vibrations to be amplified into audible sound waves. If the rapid plucking of the string by the “micro-hairs” (not to be confused with micro-taters which are equally as fun and infinitely more real) is what transfers the vibrations to the bridge, then that would mean that the faster you moved your bow across the string, the higher frequency the note would be.

It would also mean that the harmonic overtones so crucial to the unique sound of the violin would not exist, because any varying wave pattern you transfer to the bridge would be due to sporadic changes in the velocity of the bow rather than the relationship between the fundamental frequency, its integer multiples, and their geometries. Not to mention rosin would suddenly seem like a counterproductive measure. And finally, it would mean that horse hairs have horse hairs, which seems at least a bit off.

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