Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013
What is most significant is that you can hear the string as it vibrates at its resonant
frequencies. These vibrations are transmitted to a resonant chamber, like a box, which in turn
excites the neighboring air molecules. The excitation is propagated through the air as a transfer
of energy in a longitudinal sound wave. The frequencies at which the string vibrates are
translated into air pressure changes occurring with the same frequencies, and this creates the
sound of the instrument. Figure 2.12 shows an example harmonic spectrum of a plucked guitar
string. It is clear to see the resonant frequencies of the string, starting with the fundamental and
increasing in integer multiples (twice the fundamental, three times the fundamental, etc.). It is
interesting to note that not all the harmonics resonate with the same energy. Typically, the
magnitude of the harmonics decreases as the frequency increases, where the fundamental is the
most dominant. Also keep in mind that the harmonic spectrum and strength of the individual
harmonics can vary somewhat depending on how the resonator is excited. How hard a string is
plucked, or whether it is bowed, or struck with a wooden stick or soft mallet, can have an effect
on the way the object resonates and sounds.
Figure 2.12 Example harmonic spectrum of a plucked guitar string
18.104.22.168 Resonance of a Longitudinal Wave
Not all musical instruments are made from strings. Many are constructed from
cylindrical spaces of various types, like those found in clarinets, trombones, and
trumpets. Let‟s think of these cylindrical spaces in the abstract as a pipe.
A significant difference between the type of wave created from blowing
air into a pipe and a wave created by plucking a string is that the wave in the
pipe is longitudinal while the wave on the string is transverse. When air is
blown into the end of a pipe, air pressure changes are propagated through the
pipe to the opposite end. The direction in which the air molecules vibrate is
parallel to the direction in which the wave propagates.
Consider first a pipe that is open at both ends. Imagine that a sudden pulse of air is sent
through one of the open ends of the pipe. The air is at atmospheric pressure at both open ends of
the pipe. As the air is blown into the end, the air pressure rises, reaching its maximum at the
middle and falling to its minimum again at the other open end. This is shown in top part of
Figure 2.13. The figure shows that the resulting fundamental wavelength of sound produced in
the pipe is twice the length of the pipe (similar to the guitar string fixed at both ends).