The existence of so many resonances at almost random frequencies means that there is simply is no such thing as a "typical" waveform or spectrum for the sound from a violin. Indeed, there is just as much variation between the individual notes on a single instrument as there is between the same note played on different instruments. This implies that the perceived tone of a violin must be related to overall design of the instrument, rather than to the frequencies of particular resonances on an instrument.An interesting attempt to look for such global properties was recently made by the violin maker Heinrich Dünnwald in Germany. He measured the acoustic output of 10 Italian violins, 10 fine modern copies and 10 factory-made violins, all of which were excited by an electromagnetic driver on one side of the bridge (figure 4). Between 400 and 600 Hz, the factory-made violins were found - surprisingly - to be closer to the Italian instruments than the modern copies. At frequencies above 1000 Hz, however, the factory-made instruments had a rather weak response - in contrast to the over-strong response of the modern violins, which may contribute to a certain shrillness in their quality.
In practice it is extremely difficult to distinguish between a particularly fine Stradivarius instrument and an indifferent modern copy on the basis of the measured response alone. The ear is a supreme detection device and the brain is a far more sophisticated analyser of complex sounds than any system yet developed to assess musical quality.
Although such measurements give the frequencies of important acoustic resonances, they tell us nothing about the way a violin actually vibrates. A powerful technique for investigating such vibrations is called time-averaged interference holography. Bernard Richardson, a physicist at Cardiff University in the UK, has made a number of such studies on the guitar and violin. Some particularly beautiful examples for the guitar are shown in figure 5. Unfortunately, it is not easy to obtain similar high-quality images for the violin because it is smaller, the vibrations of the surface are smaller, and the surfaces of the violin are more curved and less reflective than those of the guitar.
Another powerful approach is modal analysis: a violin is lightly struck with a calibrated hammer at several positions and the transient response at various points is measured with a very light accelerometer. These responses are then analysed by computer to give the resonant frequencies and structural modes of vibration of the whole instrument. This technique has been used to teach students about violin acoustics at the famous Mittenwald school of violin making in Germany and by Ken Marshall in the US. Marshall has also shown that the way the violin is held has little effect on its resonant response.
