String Instrument Bodies

The Violin Body

The violin is probably the most studied musical instrument today, with important analyses dating back over 100 years and including contributions from Helmholtz and the Nobel laureate C.V. Raman (Helmholtz, 1954; Raman, 1918).

An excellent review of the acoustics of the violin is provided by Woodhouse (2014). Another excellent review is provided by Gough (2016).

1. Air and Wood Modes:
   • For a violin, there are typically three or four important body resonances below 1 kHz. These include the first air mode, the T1 top plate mode, and the third and fourth “corpus” modes.

     Figure 1: A comparison of admittances for two different violins.

     

   • Above 1 kHz, the mode structure is usually difficult to decipher, though a concentration of resonances around 2 to 3 kHz (the “bridge hill”) appears to be important (related to perception).

2. Tuning Top and Back Plates:
   • Various techniques exist to measure the modal frequencies of the various components (Chladni patterns, force hammers, hologram interferometry).

   • Complete systems, however, will have different mode structures than the individual plates.

   • Colin Gough has contributed a number of research papers that help explain the transition from free plate modes to complete violin-like body modes (Gough, 2015a,b,2000).

3. The Bridge:
   • The bridge transforms the motion of the vibrating string into a driving force on the top plate of the instrument.

   • The violin bridge typically has strong resonances around 3000 and 6000 Hz.

   • The bridge must move a small amount in order to transfer energy from the string to the body. For most musical instruments, however, the rate of energy transfer from the string to the bridge and soundboard is quite small (energy decay in the string is most affected by air viscosity and internal string damping).

Other Stringed Instruments

1. Guitars:
   • At low frequencies, sound radiation occurs from both plates. At high frequencies, however, most of the radiated sound comes from the top plate.

2. Electric Guitars:
   • The body has less effect on the sound. Electrical circuits replace the body filtering function.

3. Pianos: to be discussed in a subsequent week