Sound and Oscillation

# String instruments

At various times in our lives we have come across some kind of musical instrument, be it a flute, a drums, a guitar, a keyboard, etc. Instruments of this type are built for the purpose of playing musical notes according to the chosen scale. These instruments have an oscillator that, when activated, produces waves at the fundamental frequency. Subsequently, these waves undergo modifications in the resonance box, thus producing the characteristic sound of each instrument.

Stringed instruments, like the guitar, produce sounds from the vibration of their strings. When it vibrates, the string of these instruments causes the bridge to also oscillate, causing its top to vibrate, producing the audible sound.

As the top area is large, it, when vibrating, can produce sound waves with a higher volume than those produced solely by the vibration of the string, functioning as a resonance box. Each string of a guitar can vibrate producing standing waves, always having a knot at the ends where the string is fixed.

The lowest frequency mode of vibration is called the fundamental or first harmonic mode . The figure below shows the first three harmonics for a string with fixed ends.

The fundamental frequency of a stretched string is a function of its length L , its density ρ , its cross-sectional area A , and the tension T to which it is subjected. This frequency can be calculated using the expression:

In this way, it is possible to tune each guitar string by varying its tension. This is done by tuning tarraxas (pieces that adjust the tension of the strings) that are in the guitar’s hand. Stretching the string further, the frequency of vibration becomes higher, that is, the tone becomes higher.

When playing the guitar, other notes can be produced by this string, when its length is shortened, pressing the string with your finger, against the frets of the guitar fretboard. The position of these frets is such that the lengths of the string produce the entire scale of notes.

The guitar case forms the resonance box, which causes the notes played to reverberate, producing an audible sound that is slightly longer than that produced by the string alone.