When a string under tension is plucked, it vibrates back
and forth at a relatively high frequency. Waves of all frequencies travel
down and back along the string until all but a few characteristic
frequencies cancel due to destructive interference. The remaining travelling
waves form what is known as a standing wave. This entire process occurs in
very little time such that all that humans visually perceive, without
instrumentation, is the shape of the standing wave. Since both ends of the
string are fixed, two nodes, or points of no vibration, are forced at the
attachments. In addition, the string may contain additional nodes somewhere
in the middle of the string. If there are only two nodes, the string is
vibrating at the fundamental frequency. A string with three nodes forms the
second harmonic, a string with four nodes forms the third harmonic, and so
The vibration of a string continuously contracts and expands the air immediately surrounding it until all of its energy has dissipated. These air compressions, or mechanical longitudinal pressure waves to be precise, travel away in all directions and are responsible for transmitting the sound into the listener's ear. If we are to plot the pressure versus time for any point within the sound's reach, we find a sine wave. Two characteristic properties of this sine wave are detected by the ear. The first, tone or pitch, is related to the frequency. The second, peak height or amplitude, affects the perceived sound volume/intensity.
The frequency (vibrations per second) of a vibrating string is dependant on the tension applied to it, its mass per unit length, and its length. On most stringed instruments tension is adjusted by a simple rotating peg with an adjustable key. Given that length is most often held relatively constant, mass per unit length is varied by mounting several strings of differing thicknesses. Higher tension, shorter length, and a lower thickness all produce higher pitch sound waves.
In most stringed instruments, there are two principle factors contribute to the amplification of the sound volume. First, we have the structure of the box. To be specific, a faceplate and a backplate. The string vibration energies are transferred, in part, to these two plates. This causes the plates to vibrate in such a way that the emitted sound adds constructively with that from the strings. The second significant source of amplification comes from the air cavity within the box. Similarly to the investigation of the plates, resonances are formed within this air cavity. These then add to increase the overall emitted sound amplitude.
The following demonstrations attempt to teach the
concept of pitch and amplitude at an upper elementary school level. Students
will be given a short hands-on project to investigate the effect of varying
both tension and string thickness. A demonstration will then be shown to
compare the amplitudes of (i) a string mounted on a board (ii) a string
mounted on a board which is then attached to a faceplate and (iii) a string
mounted on a board which is then attached to a box.
This site was last updated 04/04/02