FEATURES Stradivarius violins are among the most sought-after musical instruments in the world. But is there a secret that makes a Stradivarius sound so good, and can modern violins match the wonderful tonal quality of this great Italian instrument? Science and the Stradivarius Colin Gough IS TH ERE really a lost secret that sets Stradivarius 1 violin basics violins apart from the best instruments made today? After more than a hundred years of vigor- force rocks bridge ous debate, this question remains highly con- bowing tentious, provoking strongly held but divergent direction views among players, violin makers and scientists alike. All of the greatest violinists of modern times certainly believe it to be true, and invariably per- form on violins by Stradivari or Guarneri in pref- erence to modern instruments. Violins by the great Italian makers are, of course, beautiful works of art in their own right, and are coveted by collectors as well as players. Particularly outstanding violins have reputedly changed hands for over a million pounds. In con- (a) A copy of a Guarnerius violin made by the trast, fine modern instruments typically cost about 19th-century French violin maker Vuillaume, shown from the player's perspective. £ 10 000, while factory-made violins for beginners (b) A schematic cross-section of the violin at the can be bought for under £100. Do such prices bridge, with the acoustically important really reflect such large differences in quality? components labelled - including the "f-hole" The violin is the most highly developed and Helmholtz air resonance. most sophisticated of all stringed instruments. It emerged in Northern Italy in about 1550, in a form that has Italian instruments restored to their former state, to recognize remained essentially unchanged ever since. The famous Cre- the vast difference in tone quality between these restored ori- monese violin-making families of Amati, Stradivari and Guar- ginals and "modern" versions of the Cremonese violins. neri formed a continuous line of succession that flourished Prominent among the 19th-century violin restorers was the from about 1600 to 1750, with skills being handed down from French maker Vuillaume, whose copy of a Guarnerius violin is father to son and from master to apprentice. The popular belief shown in figure 1 a. Vuillaume worked closely with Felix Savart, is that their unsurpassed skills, together with the magical best known to physicists for the Biot-Savart law in electromag- Stradivarius secret, were lost by the start of the 19th century. netism, to enhance the tone of early instruments. Vuillaume, Every violin, whether a Stradivarius or the cheapest fac- Savart and others wanted to produce more powerful and bril- tory-made copy, has a distinctive "voice" of its own. Just as liant sounding instruments that could stand out in die larger any musician can immediately recognize the difference be- orchestras and concert halls of the day. Improvements in tween Domingo and Pavarotti singing the same operatic aria, instrument design were also introduced to support the techni- so a skilled violinist can distinguish between different qualities cal demands of great violin virtuosi like Paganini. in the sound produced by individual Stradivari or Guarneri violins. The challenge for scientists is to characterize such dif- Back to basics: the components of a violin ferences by physical measurements. Indeed, over the last cen- To understand the factors that determine the quality of tury and a half, many famous physicists have been intrigued sound produced by particular instruments, we must first by the workings of the violin, with Helmholtz, Savart and recall how the violin works (figure 1 b). Sound is produced by Raman all making vital contributions. drawing a bow across one or more of the four stretched It is important to recognize that the sound of the great Italian strings. The string tensions are adjusted by tuning pegs at one instruments we hear today is very different from the sound they end of the string, so that their fundamental frequencies are would have made in Stradivari's time. Almost all Cremonese about 200, 300, 440 and 660 Hz - which correspond to the instruments underwent extensive restoration and "improve- notes G, D, A and E. However, the strings themselves produce ment" in the 19th century. You need only listen to "authentic" almost no sound. baroque groups, in which most top performers play on fine To produce sound, energy from the vibrating string is trans- PHVSICS WORLD Arm 2000 27 2 Kinky physics 3 Making a sound input waveform sticking regime string displacement string velocity at bowing point reflected kink bow velocity sticking III! bridge f bridge response time » slipping kink regime time - body response slipping regime bow velocity reflected LLL kink output waveform 0 12 3 4 kink frequency (kHz) time (a) Drawing a bow over the strings of a violin generates a nearly ideal sawtooth time • force on the top of the bridge. The force can consist of as many as 40 Fourier string velocity components, with the amplitude of the nth component decreasing smoothly in An exaggerated view of the transverse displacements of a bowed violin string, proportion to ~ 1/n (main figure), (b) The bridge, which transforms energy from illustrating the "slip-stick" mechanism that generates a Helmholtz wave with the vibrating strings to the vibrational modes of sound box, has a response a single kink travellingalong the string, (a) The shape of a string at five equally that varies with frequency. The resonances at about 3 kHz and 4.5 kHz boost spaced time intervals, when the kink is on the far side of the bow from the the output sound, while the dip between them reduces the "nasal" qualities in bridge. This is known as the "sticking regime". At the position where the string the tone, (c) A mathematically modelled acoustic output of the violin. The is being bowed, the string moves with the same speed, and in the same output increases dramatically whenever the exciting frequency coincides with direction, as the bow. (b) The shape of the string at five equally spaced time one of the many vibrational modes of the instrument. (cf)The Fourier intervals for the "slipping regime", when the kink is travelling between the components of the multi-resonance acoustic output, produced by bowing the bow and the bridge, and back. The string now moves in the opposite direction lowest note on the instrument at 200 Hz. The main figure shows the calculated to the bow. (c) The displacement of the string at the bowing point, (d) The force output waveform produced by the idealized input sawtooth waveform. Unlike Tsin6 exerted by the strings on the bridge as function of time, where 7 is the the Fourier components of the input, the Fourier components of the output will tension of the string. vary dramatically in amplitude from one note to the next. ferred to the main body of the instrument - the so-called strings causes die bridge to rock about diis position, causing sound box. The main plates of the violin act rather like a die otiier side of die plate to vibrate widi a larger amplitude. loudspeaker cone, and it is die vibrations of these plates that This increases die radiating volume of die violin and pro- produce most of the sound. duces a much stronger sound. The strings are supported by the "bridge", which defines The violin also has a "bass bar" glued underneadi die top the effective vibrating length of the string, and also acts as a plate, which stops energy being dissipated into acoustically mechanical transformer. The bridge converts the transverse inefficient higher-order modes. The bass bar and sound post forces of the strings into the vibrational modes of the sound were bom made bigger in die 19m century to strengthen die box. And because the bridge has its own resonant modes, it instrument and to increase the sound output. plays a key role in the overall tone of the instrument. The front plate of the violin is carved from a solid block of Getting kinky: how strings vibrate fine-grained pine. Maple is usually used for the back plate and In die 19m century die German physicist Hermann von pine for the sides. Two expertly carved and elegantly shaped Helmholtz showed diat when a violin string is bowed, it "f-holes" are also cut into die front plate. The carving of the vibrates in a way diat is completely different from die sinu- f-holes often helps to identify the maker of a valuable instru- soidal standing waves diat are familiar to all physicists. Al- ment: never rely on the label inside the violin to spot a fake tiiough the string vibrates back and fordi parallel to die instrument as the label will probably have been forged as well. bowing direction, Helmholtz showed diat otiier transverse The f-holes play a number of important acoustic roles. By vibrations of die string could also be excited, made up of breaking up the area of die front plate, they affect its vi- straight-line sections. These are separated by "kinks" diat brational modes at die highest frequencies. More import- travel back and forth along die string and are reflected at die andy, they boost die sound output at low frequencies. This ends. The kinks move witii the normal transverse-wave occurs dirough the "Helmholtz air resonance", in which air velocity, c = (T/m)i/2, where T is die tension and m the mass bounces backwards and forwards dirough die f-holes. The per unit length of die string. The bowing action excites a resonant frequency is determined by die area of die f-holes Helmholtz mode widi a single kink separating two straight and the volume of die instrument.