INTRODUCTION—
Background:
On a physical level, sound is a longitudinal
pressure wave issued from any sort of vibrating object, such as our vocal
chords, a jackhammer, or a musical instrument. These waves travel through
solids, liquids, or gasses, and move in a manner comparable to a toy slinky.
Because of the motion of these waves as they move through a given medium, the
particles of the medium become compressed in certain regions and less
concentrated in other regions. These different regions of particles are
referred to as compressions and rarefactions and can be represented in the form
of a sinusoidal wave in which time is the independent variable and pressure is
the dependent variable, as in Figure 1. (
The human perception of sound is vital in that I
allows us to navigate, detect sources of danger, and even communicate. As the pressure of
sound waves filters through the physiology of our ears, it then interpreted by
the psychology of our brains. The fundamental properties of sound perceived by
humans are intensity (volume) and frequency (pitch). Intensity refers to the
amount of energy within the wave and can be measured in decibels (dB), and
frequency refers to how often the particles of a certain medium (such as air)
are vibrating due to a sound wave, which determines how low or high a sound is
(Giancoli, 1991). Together, pitch and volume allow
human beings to determine the origin and closeness of sounds. Sometimes,
however, we encounter difficulties establishing the true source of a sound
(that is, we cannot localize the sound). On a
practical level, this inability can confuse and even
endanger us. Musically, though, it is sometimes favored when the source of an
instrument or voice cannot be detected, such as when performing in a mixed
ensemble, or when the objective of a musical piece is to create a more ethereal
feel.
Another characteristic of sound is
“timbre,” or the color and quality of a sound. Even if two
different instruments (or two different voices) are producing a sound of the
same pitch and volume, there is usually a discernable, subjective difference in
the sound; this is because each instrument and voice possesses a unique timbre,
which is influenced largely by the presence of harmonics and overtones (Winckell, 1967). A pure
tone—or sound containing one single frequency, such as one produced by a
tuning fork—contains no harmonics and resembles a perfect sine wave. But
when an instrument strikes a note or an individual sings a note, even though
only one pitch may be perceived, multiple frequencies at quieter volumes are
actually being emitted. These other frequencies are higher than the fundamental
(which is the lowest frequency) and are called overtones (Giancoli).
The frequencies of the overtones and fundamental are all summed to create a
composite waveform that resembles a “bumpier” version of a sine
wave. The different array of overtones—unique to each
instrument—creates different timbres (Giancoli).
Harmonics resemble overtones, but are instead specific integral multiples of
the fundamental frequency. When creating sound electronically, these harmonics
can be manually manipulated to create distinctive waveforms, each with unique
timbres.
One such waveform is known as a saw tooth wave
(Figure 2) and possesses every integer harmonic of the fundamental frequency.
The amplitude (volume) of each harmonic of this wave equals the inverse of its
harmonic (for example, if the fundamental has an amplitude equal to 1, the amplitude of
the third harmonic will equal 1/3). This array of harmonics gives the waveform
a rich yet “buzzy” timbre (Sievers).
Figure 3 illustrates a saw tooth wave’s spectrum with a fundamental
of 100 Hz .
Figure 2-Sawtooth Waveform
Figure 4- Square Waveform
Figure 3- Frequencies and Amplitudes of a Saw tooth Wave
Figure 5-Frequnecies and Amplitudes of a Square Wave
Yet another type of waveform is called a square
wave (Figure 4). They possess only
the odd numbered harmonics of the fundamental, but like the saw tooth wave,
also have an amplitude equal to the inverse of any
given harmonic. Sounds that result in a square wave also produce a rich sound,
but it is less “buzzy” than a saw tooth
wave and less pure than a regular sine wave (Sievers).
Figure 5 demonstrates sound spectrum of a note with a fundamental of 100 Hz
that would result in a square wave.
Statement of the Problem:
The purpose of our investigation is to determine
the relationship between the timbre of a tone and the ability to localize the
sound. Timbre will be manipulated by changing the waveform of the pitch from a
sine wave (pure tone), to square wave (containing odd multiple harmonics), and
lastly, to a saw tooth wave (containing all integral multiple harmonics). A
listener’s ability to localize the sound will be determined by how many
degrees the listeners are off from identifying the true source of the sound.
Review of Related Literature:
More than 120 years ago, John William Strutt, or Lord Rayleigh, made some progress in sound
localization by observing sounds that were sourced to the right of the
listener’s forward direction.
In this case, the left ear is in the “shadow” made by the
head, so the sound from the right is more intense than on the left, making it
possible to distinguish that the location of the source of the sound is to the
right (Hartmann). By tilting their head to the left and right in a similar
fashion, the subjects of our experiment should be able to determine the source
of the sound. Factors that may affect their ability to localize the sound
include loudness, pitch, timbre, and tone (Wightman, 1996). In our investigation, we will be keeping
the loudness, duration, pitch, and tone constant, while a manipulation of the
waveform will change the timbre of the sound.
As timbre in itself is subjective, little research
has been conducted on the direct correlation between the color of a sound and
the ability to localize it. However, researchers have found that the more
information given by a sound, the more accurately a listener can determine the sound’s
origin. For instance, a complex tone with strong harmonics will allow our ears
to simultaneously determine the size of the head shadow effect at the
fundamental and at each harmonic (
Hypothesis:
We believe that a listener’s accuracy in locating
the direction of a sound’s source will increase as timbre of the sound
becomes richer. That is, the saw tooth waveform will be localized the most
accurately, the square waveform the second most accurately, and the sine
waveform, the least accurately. This is due to the fact that the more harmonic
content there is within a sound, the more accurately an individual should be
able to locate the origin of the sound. The timbre of the tone will be the
independent variable, which we will manipulate by changing a tone from a sine
wave, to a saw tooth wave, to a square wave. The ability to localize these
manipulated sounds is defined as the direction the listener determines the
sound to be originating from—specifically, the degree of the angle this determination
is from the actual source of the sound.