[What Was Supposed To Be...The Eighth Blog] Sound.

Wow, it’s been a while... So here’s the response on sound from December that I just never got around to posting:

Values/Calculations

Instrument

Violin

Properties

Chosen string: D

- Frequency: 294 Hz

- Vibrating length: 0.32 m

- Mass density: 9.375 x 10^-4 kg/m [mass = 0.30 g]

- Tension: 33.191 N

      

Frequencies Of Next Highest Harmonics

- Second harmonic: 588.00 Hz

- Third harmonic: 882.00 Hz

    

Analysis

Fingering Positions

The fingering positions correspond to where the frequencies for the next notes can be found.  When you press the string down with your finger, it decreases the vibrating length of the string.  This shorter length results in a higher frequency.  When placed in the correct position, the new frequency is that of a new note.  For example, in first position, placing your first finger on the D-string gives the note E while your second finger can give either the F♮or F#, depending on where it is placed.

To play an E on the D-string, the vibrating length is reduced by about 0.03 m, making the new length 0.29 m.  So when the new frequency is calculated, it comes out to 324.412 Hz (which is fairly close to the established 329.63 Hz...).

Plucking/Bowing Location

The plucking/bowing location is close to the bottom (by the bridge) node of the string.  At this location...all (or most of...many of...) the harmonics are likely to be heard! :]

Plucking Versus Bowing

When a string is plucked, energy is only applied for an instant so the sound diminishes quickly.  When it is bowed, energy is constantly applied so the note can be heard for a longer period.  After the initial sound of a plucked note is heard (with all of its frequencies), some of the higher frequencies are lost so only lower and fundamental frequencies can be heard until the sound is stopped altogether.  However, when a note is bowed, all frequencies are being heard together continuously, giving it greater depth.