Harmonics of a Guitar Physics 199POM Prof. Steven Errede ...

Harmonics of a Guitar
Physics 199POM
Prof. Steven Errede
December 8, 2008
By:
Megan Abraham and Danielle Rodriguez
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The guitar is one of the most popular instruments in music today. It is used for all types
of music including rock, country, jazz, and many more. The guitar was first created in the 1500’s
in Spain. The first guitars were very small and only had four strings. The first guitars were closer
in relation to today’s ukulele. Guitars of our more recent era are made up of several different
parts that help produce the sound that we hear in today’s music industry. The guitar is made up
of a hollow body, a head (which contains the tuning pegs), the neck (which holds the frets) and
the soundboard, which allows us to be able to hear the guitar’s sound. Guitars most often have 6
strings that are attached to the bridge of the guitar and the tuners. Each of these parts helps make
the guitar’s unique sound.
All these parts play a key role in the production of sound. When the strings are plucked
on the guitar, they vibrate. These vibrations travel through the saddle (the piece of the bridge that
they are embedded in) and then to the bridge. Since the bridge is attached to the soundboard, the
entire soundboard starts vibrating. Because the body of the guitar is hollow, the sound that is
produced from these vibrations is then amplified to make the sound that we hear.
Each guitar is different in the sound that it produces. Based on the shape, type of material
it is made out of, size, and other elements, you can produce many different types of sounds on
different guitars. Another way to change the sound of a single guitar is to adjust the tuning pegs.
By adjusting the tuning pegs, you are increasing or decreasing the tension that is placed on the
string. You can also place your fingers on different parts of the strings on the finger board, to
change the notes that are being played.
In our case study, we used different means of plucking to change the sound that we
produced. We also changed the place of where we plucked the strings. We used both our thumb
over the sound hole, a pick over the sound hole and a pick over the bridge to vary our results. By
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changing the means of what we were plucking the guitar strings with, we also changed the
harmonics that were produced by the guitar. By changing the location or the way that we plucked
the strings, the vibrations that the strings produced gave off dissimilar sound waves at a given
frequency, which is determined by the density of the strings and the tension with which they are
stressed.
In this experiment we specifically observed the different harmonics of the A string of a
classical guitar. The results were somewhat expected. Using the thumb at the sound hole
produced a much louder sound than the other results. Picking at the guitar produced a clear, yet
quiet sound. Picking at the bridge of the guitar was a little different than the other results. We
saw that the picking at the bridge was very high in the 4 th harmonic as opposed to the
fundamental. This was interesting to see and provided a good variety in our results.
We used a Yamaha CG-150SA classical guitar with nylon strings for our experiment.
When we began the experiment we varied picking, using the thumb and picking the string at the
bridge for all six strings of the guitar. It would be very tedious to analyze all six strings so we
chose to use the A string because it was very rich in harmonics. We discovered this when we
measured the mechanical resonances of this guitar. To find the mechanical resonances we used a
piezo-electric transducer to put mechanical energy into the guitar to mimic the sound of that the
guitar really makes, and record the mechanical vibrations it emits.
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The first resonance peak in frequency is at about 105 Hz which closely resembles the
note A2 (110Hz). The second peak is at a frequency of ~ 235 Hz which is about an A #3 . From this
we concluded that the A string was the most rich in harmonics so we chose to observe the
different harmonics produced by the A string.
The results showed that overall the A string had a louder sound when the thumb was used
to pluck the string, it was quieter when the string was picked and that the sound was different
and quiet when it was picked at the bridge. Specifically our observations of the harmonics of the
A string showed us that by picking at the string, there was a quiet, yet clear sound.
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The harmonics associated with picking the string at the sound hole (i.e. close to the neck) are
clearer, with the fundamental as the most prevalent harmonic. Using the thumb and picking the
string at the bridge produced much different results, as shown in the figures below:
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As can be seen by comparing the above two graphs with the graph below, picking the strings of
the guitar at the sound hole/near the neck (using either a pick or thumb), the sound is a lot louder
than picking at the bridge. Picking the string at the bridge produced the most interesting results.
As seen in the following graph, the 4 th harmonic is much more prevalent/stronger than the
fundamental, which is the reason for the much different (brighter) sound when picking at the
bridge of the guitar. It is also a quiet sound because we used a pick rather than the thumb.
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Overall, this experiment tested and proved that different sounds and harmonics are
produced by varying the method of producing the sound. Plucking and picking at the sound-hole
produced much different results than picking at the bridge. It was interesting to see that the 4 th
harmonic was the major contributor when a string was picked at the bridge, which makes sense
due to the unique, bright sound that it produces. Also, the whole process of determining the
mechanical waves of a guitar was interesting to observe and understand. In the future it would be
beneficial to test different effects of at least one more string to have a comparison to the
harmonic-rich A string. However, using the A string produced the most useful data for this
experiment.
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