Making a sound
(a) Drawing a bow over the strings of a violin generates a nearly ideal sawtooth force on the top of the bridge. The force can consist of as many as 40 Fourier components, with the amplitude of the nth component decreasing smoothly in proportion to ~1/n (main figure). (b) The bridge, which transforms energy from the vibrating strings to the vibrational modes of sound box, has a response that varies with frequency. The resonances at about 3 kHz and 4.5 kHz boost the output sound, while the dip between them reduces the "nasal" qualities in the tone. (c) A mathematically modelled acoustic output of the violin. The output increases dramatically whenever the exciting frequency coincides with one of the many vibrational modes of the instrument. (d) The Fourier components of the multi-resonance acoustic output, produced by bowing the lowest note on the instrument at 200 Hz. The main figure shows the calculated output waveform produced by the idealized input sawtooth waveform. Unlike the Fourier components of the input, the Fourier components of the output will vary dramatically in amplitude from one note to the next.