The guitar produces sound through vibrations. When a string is plucked, it vibrates and transfers the vibrations to the bridge and inside the guitar body. These vibrations cause the air inside to vibrate, producing sound. The guitar has evolved over time from its early creation in 1779 by Gaetano Vinaccia to the modern acoustic guitar design by Antonio de Torres in 1850. Les Paul further innovated the guitar by adding microphones, and George Beauchamp created the first electrically amplified guitar in 1936. Mathematics plays a role in the guitar's complex shapes and materials that affect resonance and sound. Equations relate the wavelength and frequency of vibrations as well as the tension and speed of the string's waves.

1. The Guitar
By: Andres Sanchez
Ms. Sullivan
5-15-13

2. How?
Just like a speaker, the sound is created through
vibrations inside the body of the guitar. The
vibrations are created when playing a string, the
string vibrates and transfers it on to the bridge.
On the inside of the body, the vibrations make
the air make that sound. But the smaller the
string the more higher(Pitch) will sound. Just like
the arp , the strings get and it sounds more high
pitched, just like the guitar.

3. How?

4. What?
On present day, the guitar is one of the most
famous stringed instrument on the world. Its
easy to learn and really needs multi-task brain
to play it good. Just like any instrument its been
there for many generations since 1779 when it
was created on its earliest form.

5. Who?
Nepolitan decent, Gaetano Vinaccia created the
guitar on its early form on 1779. Later on 1850
Antonio de Torres Jurado created the present
day acoustic guitar. After a while ,Les Paul, a
guitar inovator experimented putting
microphones on guitars. The first electrically
amplified guitar was designed by George
Beauchamp in 1936.

6. When?
Gaetano Vinnaccia born in 1759, and had a family that selled
mandolins. Gaetano decided to “upgrade it” making an early version
of our guitar. Antonio de Torres born in June, 13, 1817, in La Cañada,
Almeria. George Beauchamp, who was born in March 18, 1899.
Year What
1779
1850
1936
Who What
Gaetano Vinaccia Created the early guitar.
Antonio de Torres Upgraded the guitar to present guitar.
George Beauchamp Created the first electric guitar.

7. Why does this relates to math?
Once you think about it, everything has math.
Even the most basic thing has math, the guitar is
a complex object mathematically. Every single
shape, material, and even air, all affect the math
of the guitar. Inside the body, there are
complex shapes in it so there would be a better
resonance on the sound. Every part in it has an
important role. Basically its one of the most
complex instruments that uses all this math.

8. Some equations to find relationships
Relationship between wavelenght & frequency:
V=FW
V is the speed of wave. F is the frequency. W is
the wavelenght.
Relationship between speed and tension:
V=TM
V (squared)is the speed of wave. T is the tension
of the string. M is the mass density.

9. I play guitar too

10. Bibliography
Books: “Simply Guitar” by Steve Mackay.
Encyclopedia:
http://www.britannica.com/EBchecked/topic/1
20212/classical-guitar
Website:
http://www.ehow.com/facts_4743458_guitar-
facts.html
http://ezinearticles.com/?Guitar-
Information&id=7521495