The very basis of all instruments originates in Physics. Whether the instrument is a piano, flute, or violin, the mechanics of its sound can be understood by looking at the Physics behind it. The violin is an instrument consisting of four strings with four different frequencies. The strings are classified as G, D, A, and E. The equations of physics can be used to correlate playing a violin and understanding the physics behind what is occurring. The way to make a musical sound is to have something vibrating. Since the violin is not an electronic instrument by nature, it requires combinations of standing waves. The strings on a violin are stretched very tightly and vibrate at great speeds, thus making it difficult to realize what exactly is happening. Researching information on this project was very appealing to me as a violinist. It helped me to learn the mechanics of the instrument that I have been playing for years. The violin originated in medieval ages and was a "fiddle" of the minne-singers. This instrument resembled a violin but did not actually look like the violin we know today until the 16th century during the Renaissance. The Italians and spread across the continent of Europe. Through experience when playing a violin for so many years, it is noticeable that the older the violin is, the richer the sound. The reason that this is true is astonishing and probably unimaginable. It has to do with pollution of the environment. Because violins are made from wood, nutrients which are in the wood remain there even when it is dried out. As centuries went by, the pollution from increased industrialization gave a greater risk of weak wood. The substances in wood nowadays are looked over as unimportant because of increased demand of the instrument. It's a helpful tip if this project irks you to learn how to play the violin to make sure you buy the oldest possible one available. The main content of this project is to understand the physics behind playing the violin.
Through this project it will be easier to understand:
1. Traveling waves (such as when the string is plucked)
2. The motion of a string when it is bowed rather than plucked
3. Antinodes and Nodes of traveling and standing waves
4. Harmonics and Frequencies based on wave lengths and modes
5. What happens when a violinist she puts her finger down on the fingerboard?
6. How to find the frequency of a note based on the harmonic, length, and mass
It is evident therefore, that the equations that we have learned this year will greatly help us to understand the physics of violins.


1. Traveling waves and Standing Waves
The experiment that we did in class recently with the slinky is a very useful way to understand
two travelling waves add to give a standing wave
two travelling waves add to give a standing wave
the mechanics of a traveling wave. If you hold both ends of the slinky down and pull it to the side, it will create something that looks like a wave. It will travel away from you and then reflect back and travel towards you. If the slinky is stretched more, with more tension, there will be a faster traveling wave. In the same way, a string which has more tension than another, will travel faster and have a higher frequency. The importance of the wave traveling back towards you is that the wave is inverted. Because the string is being fixed in place by the tailpiece (see picture), it will have an inverted reflection. The image on the right is a diagram of what happens as time passes. The Green and Blue lines and two different waves while the red line is the sum of these waves. The interaction of both waves cause either constructive or destructive interference. In music, constructive interference is harmony while destructive is simply noise and cacophony. The Nodes and Antinodes of each stage are labeled in the diagram.

2. Bowed String vs Plucked String
There are generally two ways to play the violin. To pluck the string is to simply take your finger and let go of the string. Plucking on the other hand, loses all of the energy quickly and the sound is quickly gone.
animation of stick-slip motion
animation of stick-slip motion
The bow is a part of the instrument and is very important to the sound. Because of a bow, a sound can be held constant at a specified loudness. The modern bow has a "hatchet" head which allows for even distribution of the force. The cycle of the bow involves slip-stick-slip-stick. The stick portion of the cycle deals with static friction while the slip is kinetic friction. You may have seen a violinist put a chalky material on the bow called rosin. Rosin lowers the kinetic coefficient while increasing the static coefficient, making the difference between the two very distinct. With high static friction, the bow sticks to the string and carries the string with it. Because this happens, the string moves with the bow. When the kinetic friction acts on the string, the string moves towards the end of the violin and reflects back. It is important to realize that the slip-stick cycle does not refer to the bow going up and down. There are innumerable slip-stick cycles in one bow motion.

3. Harmonics and Modes of different Frequencies
Because the string of a violin is fixed at both ends each end has a node. Because of this limitation, the frequencies of the strings are usually half of the wavelength.

For instance, a string with length L will have double the wavelength because wavelength = 2*length. For any wave the frequency is a ratio between the speed of the wave and its wavelength. Therefore, f = v/wavelength.

The speed of all of the waves are the same and the frequencies and wavelengths are variable.

4. Putting Finger down on the Fingerboard
When a violinist puts her finger down on the fingerboard at a certain point on the violin, it produces a standing wave identified with a certain
wavelength and frequency. This image exaggerates the vertical axis of the violin but shows what is occurring when a finger is placed on the fingerboard. The place where the finger is pressed creates an antinode. The reason that learning the violin is so difficult is that there are so many wrong places that a finger can be put. If one is slightly off in finger placement, it creates a frequency that may not even be a particular note. Only when the finger is placed in an accurate position is a frequency delivered which is most commonly known as a note. This note has a particular frequency that if produces and based on the equation v = f*wavelength, has a constant velocity and variable wavelength.

5.How to find the frequency of a note based on the harmonic, length, and mass
It is important to connect all the learned aspects of harmonics into an easy method to figure out a particular measurement. If one wants to find the frequency of a particular note, one must follow the next equation. Suppose the vibrating string has a length L, mass of M, tension of F, and played at the nth harmonic.
fn = (n/2L)(FL/M)1/2 = (n/2)(F/LM)1/2
This equation connects all of the aspects of a string to figure out the frequency.
On the other hand, if one wants to figure out the force of tension of a string one can use:
F = 4f12LM.

Incredible Performance! \/

Understanding the physics and mechanics of the violin is extremely vital because it gives a background knowledge in knowing what is occurring when you are either plucking or bowing a string. It helps to provide explanations for a certain note sounding the way it does. It also helps appreciate the beauty and art of being able to play a string instrument such as the violin whose mechanics are relatively simple and yet created a magnificent sound.

Questions and Answers
Sonia Bansal - Do you ever play two of the strings at the same time and if so, how do those two strings become one sound?
Yes you can play two strings at the same time. They don't necessarily become one sound but this is the way you can produce chords. It's also the most common way to tune the instrument because after a while your ear is trained to hear a certain sound when the two strings are played together. The two notes, if they are just two open strings, make a fifth because logically they are 5 notes apart. A lot of times you'll play two strings together and put your finger down on one of the strings and realize that's not such a pretty noise and sometimes you'll play two notes and it sounds like harmony. That's the difference between constructive and destructive interference.

Brandon Siegenfeld- Are there other artificially made violins that produce equal or better sounds than old wood ones (I saw a history channel show about a carbon fiber string instrument, I think it was cello, however it did not say if it produced better sound quality)?
The material of a violin has a direct correlation with the sound that it produces. The better the quality, the better the tone. Sometimes, if the old violins are made of bad material then the artificial would be a better choice, but this is rarely true.

Robert Lopez - Does the type of material used to make the string affect the harmonics(are there even any other types of strings or are they all the same?)?
The material doesn't affect any of the scientific aspects such as harmonics, wavelength or the frequency. It does however affect the quality of the sound.

James Song- Why does lightly placing a finger on the string produce a ringing harmonic, as opposed to pressing down on the string?
When you place your finger on the string, it creates a node that is halfway between the actual note and the harmonic. When you put your finger down completely, it no longer doubles the frequency, it creates a new node with a completely different frequency. That's why playing a harmonic is when you put your finger half way on an open string so that frequency is doubled.

Kevin Norris - Why does placing a finger on the finger board create an antinode and not a node?
Where the finger is placed is one node of the string. The other node is the other end of the violin where the fine tuners are.

Greg Sturm - I used to play the violin, I was terrible at it. Good memories though. Anyway, why is the bow made of horse hair as opposed to some other material?
Haha, it can be a tedious instrument to learn. The horse hair gives more sound when combined with rosin which gives the bow its friction. I'm pretty sure they make bows with different materials now but horse hair is most common

William Chan asks "How do the harmonics of a violin differ as compared to other string instruments such as the cello?"

Sam Edwards - How/why do the nutrients in the wood effect the sound that a violin makes?

Ari Horowitz - Since the wood nowadays is becoming weaker, why are the majority of violins still made from wood?

Philip Cohn-Cort - I'm sorry, but the equation given under section 5 seems a bit arbitrary. Perhaps you could elaborate? On a different note, what is the best distance to keep when listening to a violin player, for quality of sound and the artist's ease of playing? (I know it varies, but still...)

Douglas Chin - What would happen to the sound if the two F-holes were covered and not open?