1. Soundboards Function is to amplify the sound of vibrating strings –A surface pushes more air than a string, thus it is a more efficient radiator of sound String vibration must be efficiently transmitted to soundboard –Soundboard cannot be too heavy, thick, or wimpy –Connection to strings must be strong Plates have complex standing wave patterns –Response curve of plate determines which frequencies are amplified the most –Does not follow the harmonic series –Ideal response is to amplify all frequencies more or less equally –Plates with very little damping (like metal) have sharp response peaks - not good

2. Standing waves on plates (Chladni patterns) Images by Thomas Erndl Published at http://www.phys.unsw.edu.au/~jw/guitar/patterns_engl.html

3. Response curve 2 complete violins Violin belly Images produced by Ra Inta and Joe Wolfe Published at http://www.phys.unsw.edu.au/jw/violintro.html Helmholtz resonance of violin body

4. Resulting amplified sound

5. piano soundboard

6. Resonators Helmholtz resonator is basically a cavity with an opening Acts like mass+spring Single frequency response Most often provides “bass boost” in stringed instruments http://www.darntonviolins.com/violinmaking.php

7. Transmitting the vibration Ideal characteristics: - very stiff (rigid) - very light - small area of contact with the top plate You don’t want to waste energy on making the bridge vibrate

8. Standing waves in rooms Pairs of opposing walls form the boundaries of standing waves 3 sets of standing waves in a rectangular room Frequency of nth harmonic: c = 340 m/s = 1100 ft/s in air