This diagram shows how the sound waves travel through its medium. (Sound always requires this medium so that the particles can vibrate, and carry the wave. Therefore sound cannot travel through a vacuum.) As sound is a wave it follows the many rules of waves, these include the importance of frequency and wavelength. As in all waves, the wave equation applies. The speed of the wave equals the wavelength multiplied by the frequency: -
v = f
When making music sounds are created, this is due to the travelling waves from the instrument. In the case of a wind instrument such as the recorder the particles that are moving are the air molecules inside the instrument. As the player blows into the recorder the air molecules begin to vibrate, and the wavelength depends on the tube length, or where the covered hole on the recorder is. In any instrument there is a fundamental wave, this is the wave with the lowest frequency that can be produced by any particular musical instrument. This fundamental wave is known as a standing wave, this is a wave that seems to be constant; i.e. it does not move. In the case of a recorder, or other open tubes the fundamental wavelength is equal to twice the length of the tube. In the case of a recorder changing the positioning of the fingers on the instrument alters the wavelength. This will also change the frequency, and therefore the pitch of the note.
Standing waves do not only have fundamental frequencies but also harmonics. Fundamental waves are very important in stringed instruments, such as guitars, as are their corresponding harmonics. The fundamental wave can be simply described as the smallest wave that can be produced on a length of wire. The length of the fundamental wave is equal to ½ , the length of the first harmonic is and the second harmonic is 3/2.
By looking at the diagram it is evident that certain parts of a standing wave do not move at all, these parts of the wave are known as the nodes, but other parts move a great deal, these are known as the antinodes. It can be said that the reflection of a standing wave is in antiphase to the original.
There are three different ways of changing the frequency of a fundamental wave; these are by changing the length, thickness or tension of a given wire. This is very important when playing the guitar, or other similar stringed instrument. Musicians often have to alter these factors to create the note(s) required. The length of the string can be altered by holding the string at different places, thus changing the pitch of the note produced. When tuning a guitar the tension is often altered, and the use of a tuning fork helps to find the correct note.
The three important factors can all be linked to the frequency via an equation: -
Different instruments use different lengths of string or columns of air to produce different pitches and sounds. For example the Banjo has shorter strings than a guitar so therefore produces higher notes. Other instruments produce many different sound waves at the same time (an oboe for instance) these sine waves combine to create a waveform. This means that several harmonics are produced together to create the final sound.
Michelle 12MA Page October 2001
