Guitar Strings and Harmonic Waves

2. WHAT IS A HARMONIC WAVE?
• A harmonic wave is a wave that is generated
by a source that is undergoing simple
harmonic motion.
• It can also be referred to as a sinusoidal
wave.
• The oscillation of the source results in a
continuous wave.
• Can be represented by both sine and cosine
functions.
• Every harmonic wave has a wavelength (the
shortest distance it takes for the shape of a
wave to repeat itself).
• These waves have what is known as
“harmonics”.
• Harmonics are characterized by a wave that
has a frequency which is an integral multiple
of the frequency of some reference wave
(Rouse 2005).

3. GUITAR STRINGS AND HARMONIC WAVES
• Guitar strings can exhibit harmonic waves.
• The various frequencies allow for different and
distinct sounds to be heard.
• These frequencies can be translated into “octaves”
which give us high or low pitched sounds.
• An octave is the interval between one musical pitch
and another with half or double its frequency
(Sachs and Kunst, 1962).
• These different octaves and frequencies give the
acoustic guitar a unique and echoing sound.
• Each note played on the guitar will have a different
frequency and wave function. (for example the note
middle C has a frequency of 261.63 Hz, while the
lower pitch note A has a frequency of 220.00 Hz).
• Each note also has an associated speed of the
pulse asscoiated with it, due to each notes unique
frequency and wavelength.

4. QUESTION 1
Based off the knowledge from this week’s pre-reading, recall that the speed of a
wave is given by the equation v= λƒ. If a guitar player is playing a note (for example
C), and then increases the note’s octave by one (correlating to a decrease in
wavelength by a factor of ½,) what happens to the speed of the wave when the
guitar player plucks the string?
a) The speed increases
b) The speed decreases
c) The speed remains unchanged

5. ANSWER
• The answer to the previous question is c) The speed remains the same.
This is due to the relationship between frequency and wavelength. If the
wavelength is decreased by a half, then the frequency, being inversely
proportional to the wavelength will be two times the amount. Thus, we
come to the equation
v=(1/2) λ*(2ƒ)
Which simply equals
v= λƒ
Therefore, despite the change in the values for the frequency and
wavelength, the speed of the pulse will remain the same.

6. REFERENCES
Rouse, M. harmonic. http://whatis.techtarget.com/definition/harmonic
[accessed Sunday February 8th 2015].
Sachs, C. and Kunst, J. (1962). Cited in Burns, Edward M. (1999), p.217.