And of course, if a node is added to the pattern, then an antinode must be added as well in order to maintain an alternating pattern of nodes and antinodes. The second harmonic of a guitar string is produced by adding one more node between the ends of the guitar string. The diagram below depicts this length-wavelength relationship for the fundamental frequency of a guitar string. This is the case for the first harmonic or fundamental frequency of a guitar string. The pattern is the result of the interference of two waves to produce these nodes and antinodes.) In this pattern, there is only one-half of a wave within the length of the string. Thus, it does not consist of crests and troughs, but rather nodes and antinodes. A standing wave pattern is not actually a wave, but rather a pattern of a wave. ( Caution: the use of the words crest and trough to describe the pattern are only used to help identify the length of a repeating wave cycle. A complete wave starts at the rest position, rises to a crest, returns to rest, drops to a trough, and finally returns to the rest position before starting its next cycle. If you analyze the wave pattern in the guitar string for this harmonic, you will notice that there is not quite one complete wave within the pattern.

The diagram at the right shows the first harmonic of a guitar string. The fundamental frequency is also called the first harmonic of the instrument. The lowest frequency produced by any particular instrument is known as the fundamental frequency. This would be the harmonic with the longest wavelength and the lowest frequency. The most fundamental harmonic for a guitar string is the harmonic associated with a standing wave having only one antinode positioned between the two nodes on the end of the string.

In between these two nodes at the end of the string, there must be at least one antinode. Subsequently, these ends become nodes - points of no displacement. Because the ends of the string are attached and fixed in place to the guitar's structure (the bridge at one end and the frets at the other), the ends of the string are unable to move. Recognizing the Length-Wavelength RelationshipДЇirst, consider a guitar string vibrating at its natural frequency or harmonic frequency. We will see in this part of Lesson 4 why these whole number ratios exist for a musical instrument. This is part of the reason why such instruments sound pleasant. For musical instruments and other objects that vibrate in regular and periodic fashion, the harmonic frequencies are related to each other by simple whole number ratios. At any frequency other than a harmonic frequency, the resulting disturbance of the medium is irregular and non-repeating. These patterns are only created within the object or instrument at specific frequencies of vibration these frequencies are known as harmonic frequencies, or merely harmonics. Each natural frequency that an object or instrument produces has its own characteristic vibrational mode or standing wave pattern. Whether it is a guitar sting, a Chladni plate, or the air column enclosed within a trombone, the vibrating medium vibrates in such a way that a standing wave pattern results. Previously in Lesson 4, it was mentioned that when an object is forced into resonance vibrations at one of its natural frequencies, it vibrates in a manner such that a standing wave pattern is formed within the object.

Harmonic