# Course:PHYS341/Archive/2016wTerm2/The Contribution Of F-holes To A Violin's Sound

The Contribution Of F-holes To A Violin's Sound

The violin is a stringed musical instrument that has two f-holes. The f-holes, sound holes shaped like the letter f, and carved on each side of the violin’s body, as shown in Fig.1 and Fig.2, act as Helmholtz resonators to project sound more clearly, when a string is either plucked or bowed.

Fig.1. The whole body of a Gliga violin.
Fig.2. Both F-holes on a Gliga violin. F-holes act as Helmholtz resonators.

### How F-holes work as Helmholtz Resonators

A violin's two f-holes, located to the left and right of the bridge, act as Helmholtz resonators, or air-filled cavities that have a neck. In other words, f-holes contain a mass, or neck, which is the air in and around the f-hole[1][2], and the spring, or the cavity air, which is the air inside the body of the violin. They also allow air to bounce in and out, and extension of island flexibility and mobility[3][4].

Fig.3. The harmonic spectrum of a violin's E-string, with both f-holes open. The fundamental frequency of an E-string is 660 Hz, hence each harmonic that is seen has a integer value of a multiple of 660. The second harmonic has a frequency of 1320 Hz, the third a frequency of 1980 Hz, and so on.

### The Shape of an F-hole

Introduction of holes to string instruments has a long history, dating as early to the 10th century in Medieval Europe, starting with the circular holes, before the shape of the holes eventually began to evolve from simple geometrical shapes during the 16th through the 18th century, into f-holes, which are currently being used in string instruments, namely the violin and other related musical instruments[5].

First and foremost, the body of a violin is a radiator of sound[6], and the volume of air inside the box vibrates as soon as energy reaches the violin body and the wooden surfaces vibrate, which produces pressure fluctuations that spread to other parts of the cavity. These pressure fluctuations eventually leave through the f-holes. The A0 (main air) resonance, or the standard Helmholtz resonance for all violins is approximately 290 Hz, or a D4[7][8][9], which is close to the natural resonance frequency of the second string of the instrument. The A0 is also the only cavity mode which resonates most strongly through the f-holes. F-holes allow acoustic energy to get out as a result of copulation of string vibration, and maximization of the flow of sound. Additionally, wood resonances, a vibrational mode of the wooden body of the violin, along with air resonances, allow f-holes to radiate, amplify and control the sound of a violin at a particular frequency[10].

Fig.4. A comparison of the fundamental frequencies of a Gliga violin's E string. a) When both f-holes are blocked, the fundamental frequency of a bowed E-string decreases from 660 Hz to approximately 655 Hz. b) When one f-hole is blocked, the fundamental frequency of a bowed E-string decreases from 660 Hz to approximately 657 Hz. c) A violin's E-string fundamental frequency (660 Hz), both f-holes open, when bowed. Despite the results, the f-holes generally have little to do with the violin's fundamental frequency.

F-holes have also been suggested to be important for decreasing the frequency of the lowest radiating mode, and adding an extra resonance to the violin body related to the Helmholtz resonance. F-holes increase radiation damping of outlying harmonics which may interfere with the audibility of sound[11]. Bissinger (1998) discovered that when the f-holes were open, the A0 decreased. Although Fig.4 shows that f-holes generally have little to do with the fundamental frequency of a violin itself, on the other hand, f-holes play a contribution in the amplitude of the sounds of violins. Johnston (2009) observed that blocking holes with tissue or cotton wool resulted in reduction in loudness[12], while Vandegrift discovered that the amplitude as a result of placing tape on one of the f-holes resulted dropped by approximately 14 dB[13]. Similarly, as shown in Fig.5, which make comparisons of the amplitude of bowed strings when both f-holes, one f-hole and no f-holes are covered respectively, blocking an f-hole has caused the amplitude of a bowed string to decrease.

A factor that has been said to account for the shape of the f-hole is f-hole length[14]. Although it was discovered that a decrease in f-hole length lowered resonance frequency, and an increase in f-hole length led to an increase in resonance frequency, an f-hole that is too long leads to radiation damping. Hence, if an f-hole is too long, there may be excessive damping of harmonics essential for producing certain frequencies from a violin when its strings are plucked or bowed. After testing f-holes of different lengths, it has been observed that 11 to 14.3 mm would be an ideal diameter of width of the holes, and an ideal length would be around 75mm, in order to keep the resonance frequency at 290 Hz[15][16].

Fig.5. A comparison of the amplitudes of a Gliga violin's D string. a) When both f-holes are blocked, the amplitude of a bowed D-string is approximately -20 dB. b) When one f-hole is blocked, the amplitude of a bowed D-string is approximately -18 dB. c) The amplitude of a bowed D-string, both f-holes open, is approximately -14 dB.

Overall, f-holes are essential for resonance of air with the neck and the cavity, and give the violin its distinctive timbre.

## References

1. Curtin, Joseph, and Rossing, Thomas D. “Chapter 13: Violin.” The Science of String Instruments, edited by Thomas Rossing, Springer, 2010, pp.230.
2. Coffey, John. “The Air Cavity, f-holes and Helmholtz Resonance of a Violin or Viola.” 2013, pp.30-35.
3. Gough, Colin. “A violin shell model: Vibrational Modes and Acoustics.” The Acoustical Society of America, vol. 137, no. 1210, 2015, pp.1210-1225.
4. Beament, James an Unwin, Dennis. “The hole story.” Strad, vol. 112, no. 1332, April 2001, pp.408.
5. Nia, Hadi T. et al. “The evolution of air resonance power efficiency in the violin and its ancestors.” Proc. R. Soc. A, vol.471, 2015, pp.5-10.
6. Johnston, Ian. “Interlude 3: the violin.” Measured Tones: The Interplay of Physics and Music, CRC Press, 2009, pp.127-129.
7. Chen, Mo et al. “Vibrational behavior of a soundbox in an atmosphere with a variable speed of sound.” The Journal of the Acoustical Society of America, vol. 131, 2012, pp.2495-2499.
8. Vandegrift, Guy. “Experimental study of the Helmholtz resonance of a violin.” American Journal of Physics vol. 61, 1993, pp.415-421.
9. Eargle, John N. “Music, sound, technology.” Springer, 1995, pp.88.
10. Benade, Arthur H. “Instruments of the Violin Family.” Fundamental of Musical Acoustics, Oxford University Press, 1976, pp.528-534.
11. Nia, Hadi T. et al. “The evolution of air resonance power efficiency in the violin and its ancestors.” Proc. R. Soc. A, vol.471, 2015, pp.11-26.
12. Johnston, Ian. “Interlude 3: the violin.” Measured Tones: The Interplay of Physics and Music, CRC Press, 2009, pp.127-129, 182.
13. Vandegrift, Guy. “Experimental study of the Helmholtz resonance of a violin.” American Journal of Physics vol. 61, 1993, pp.415-421.
14. Nia, Hadi T. et al. “The evolution of air resonance power efficiency in the violin and its ancestors.” Proc. R. Soc. A, vol.471, 2015, pp.11-26.
15. Nia, Hadi T. et al. “The evolution of air resonance power efficiency in the violin and its ancestors.” Proc. R. Soc. A, vol.471, 2015, pp.12-14.
16. Coffey, John. “The Air Cavity, f-holes and Helmholtz Resonance of a Violin or Viola.” 2013, pp.37.