Looking at the models of bridge ascribed to Stradivari bearing in mind mechanical wave propagation, they appear to be a very sofisticated design:
Models for cello
Models for violas Models for violin
The shape of a bridge
The rol of the bridge is bringing the soundwaves created by the vibration of the strings to the body of the instrument. The shape of a bridge is a set of mirrors, whose function is reflecting waves in a certain way.
Opposite to the modern bridge, where holes are placed so to make the way of the waves until the feet of the bridge a long one, Stradivari models make this way so direct as possible.
In the next picture I have drawn rings product of the vibration of a string. These rings are the propagation in all directions of mechanical waves from the origin of the vibration.
In the next picture I have drawn some of these trajectories. The most direct way (with less reflections) goes crossing the bridge: mechanical waves from the left side strings go down by the right foot, right side strings' waves by the left one.
A paper model becomes wood
How the Strad models must be adapted? From where must wood be cut out to make the models become real bridges?
Looking at the bridge for the viola tenore of the Tuscan quintet made by Stradivari and comparing it with its model (notice
that the curve has been later modified to adapt it to the use of modern strings) they appear to be very much the same:
Here is another example:
Click on the next click-to-enlarge image to see in full size the radiography of the Tuscan tenore, so to see the placing of the foot of the bridge respect to the harmonic bar:
The bridge of the Tuscan tenore
The profile of the bridge of the Stradivari's Tuscan tenore was in wedge form, the back perpendicular to the instrument, the front of the bridge opening in a 5,5° angle to the back. Both front and back were flat, which means that the curve where the strings lie on could be thinner at the top and thicker at its lowest parts, the sides of the bridge. The original curve was later modified, I supose to adapt it to the use of more modern strings, making impossible to know how this curve really was, with the same thickness all along or indeed thinner in the middle and thicker at its sides. The bridge is now completely bent. The corners of the bridge are left at 90°. This kind of profile, two opening straight lines, optimizes the propagation of mechanical waves, for at each rebound they are reflected in a more open angle, minimizing so the number of rebounds front-back.
Stradivari used for his bridges flamed maple. Striped maple, the wood used at the present day, is a very good waves conductor suitable for modern bridges, but producing a too bright sound with Stradivari models.
I call it in English "harmonic bar" –as it is called in some languages– instead of "bass bar" because if it has to be called with a name of frequences it should be called "treble bar", because these are the frequences that arrive to it in the most direct way. The first frequences that get lost in the distance and suffer more at being disturbed are the trebles, suffering more the softer the matter they travel through is, that's why softer materials produce a darker sound. Thus the place of the harmonic bar makes a lot of sense, helping trebles to get distributed all along the front. Bass frequences go through the sound post to the back of the instrument.