Guitar strings create musical
sound through vibration, as we
have just learned. Understanding how strings
work with frets to create specific
vibrations (and therefore specific tones) will
help you to understand why a
guitar sounds the way it does, instead of like a
kazoo or an accordion.
Every Musical instrument has
some part of it that moves in a
regular, repeated motion to produce sound. On a
guitar, this is where the
strings find their purpose. A string that you
bring to a certain tension and
then set in motion by a plucking action produces
a predictable sound. If you
tune a string to a different tension, you get
different tones. The greater the
tension is, the higher the pitch. This is the
sole purpose of the tuning pegs on the guitar's
headstock.
However, you couldn’t do very
much with a guitar if the only
way to change pitches was to frantically adjust
the tension of the strings
every time you pluck a string. So guitarists
resort to two main ways to change
a string’s pitch. To identify these ways we will
first derive the equation that
relates to the frequency of these vibrations.
The first important equation to
consider is the relation vstring= √(Ts/µ),
where Ts
is the tension in the
string, and µ (µ = mass /length)
is the linear density of the
string. Since we stated earlier that v= λf, we
can now say that: f =
[√(TsL/m)] / (λ).
Guitar strings utilize these
fundamental properties of waves to
produce the correct pitch, or frequency, of
the desired note. If the tension in
the string remains constant, the easiest ways
to adjust the frequency is by
adjusting the mass of the string, or by
adjusting its effective vibrating
length.
From our
equation, we can see
that the more massive the string, the lower
the resulting frequency will be. In
other words, the thicker strings on a guitar
produce lower notes, and the
thinner, less massive strings produce higher
notes. Similarly, by adjusting the
effective vibrating length of a string, you
adjust the wavelength, λ, that the
string vibrates with. The larger the
wavelength, the smaller the frequency will
be, and vice versa. In playing, this is
adjusted by holding the strings firmly against
fingerboard, pressing the strings against the
frets.
