After that preamble we are ready to look in detail at some specific types of measurement. We will start with a group of methods concerned with exploring structural details that, for one reason or another, cannot be seen with the naked eye. There have been huge developments in recent decades in ways to visualise hidden details, and we will show examples of some of the most striking in this section. The measurements rely on seriously expensive laboratory-grade equipment, but the results are so useful to instrument makers that images like the ones we will see are becoming quite familiar in that world.
First, we will look at microscope imagery, applied to the cellular structure of wood and how this is modified by wood-working procedures. Traditional light microscopes have, of course, been with us for a very long time. Wood cells can be viewed that way, but there are two drawbacks. First, the use of light puts a limit on the highest magnification you can use: the wave nature of light means that it is not possible to image details once their length scale becomes comparable with the wavelength. Secondly, at least with traditional microscopes, there is a severe limitation on the depth of field of the images you obtain.
Both these drawbacks can be circumvented by using a scanning electron microscope (SEM). Shorter length-scales can be seen, although there is still a limitation for viewing a relatively fragile material like wood, because to see shorter and shorter scales you need to fire your electrons with higher and higher energy. Beyond a certain point this causes damage to the specimen you are trying to see. Secondly, for technical reasons to do with the way electron microscope lenses work, SEM images can have a very large depth of field. This gives images with a very striking and satisfying three-dimensional character.
I will show samples of SEM images here: the next link gives a more extensive picture gallery. I am grateful to Claire Barlow for doing the microscopy for all these images. Figure 1 shows an image we saw earlier, a general view of the cell structure of Norway spruce (Picea abies), a wood commonly chosen for soundboards of stringed instruments of all kinds. Three red arrows identify the three principal directions in the tree: the L direction runs vertically in the tree, the R direction runs radially, and the T direction runs horizontally around the tree trunk in a direction tangential to the annual growth rings and the bark of the tree.
Softwoods like Norway spruce have a relatively simple structure, dominated by two types of cells. The majority are tracheids, long tubes running vertically in the tree, tapering down to a point at both ends. Running perpendicular to the tracheids, oriented in the radial direction in the tree, are rays. In spruce the ray cells are typically stacked in vertical columns, just one cell thick. You can see one of these stacks in Figure 1, just left of centre in the lower part of the image. It has been sliced through by the knife cut used to prepare the wood sample for the microscope. We will see a clearer example in a moment, in Fig. 3.
In Fig. 1, the R arrow is shown pointing in the outward direction from the centre of the tree. This is the direction in which the tree grows. New tracheids are formed on the outer edge of the tree trunk, just below the bark. In the spring the tree grows rapidly, making new tracheids that are large and thin-walled. As the growing season progresses, the growth rate slows down and the new tracheids have thicker walls and less internal space, until growth stops altogether. It bursts back into action the following spring. This modulation of the tracheid geometry is responsible for the annual growth rings of the tree: it can be seen clearly in Fig. 1, and in more detail in Fig. 2 which shows about 2 complete annual cycles.
Figure 3 shows a different view of all these features. This time the wood has been cut approximately in the LR plane: this orientation of cut would normally form the visible outer surface of the soundboard in a violin or guitar. Tracheids make the obvious “tunnels” heading towards the top right-hand corner of the image. Immediately on the “roof” of these tunnels we see a ray: a stack of about 5 cells have been exposed by the cut, heading towards the top left corner. There are other anatomical details visible in these pictures, but I won’t discuss them here: see the previous link.
In section 10.1 I said that every measurement has pitfalls for the unwary, with the possibility of misleading results. I will conclude this discussion of SEM images with a few words about problems that can arise with those. A normal electron microscope relies on the specimen being able to conduct electricity, but of course wood is an insulator. In order to obtain images like these, the specimen has to be coated with a thin layer of conducting material, usually gold. Not enough coating, and the images will show artefacts of “charging”: the electrons that have been fired at the specimen cannot escape, and they give an electrical charge which can distort the image. To much coating, and fine details of the structure you are trying to see might be covered up.
Another snag is that the SEM works best when the chamber containing the specimen is pumped out to give a high vacuum. This removes air molecules that might interfere with the electrons, but vacuum might also affect your specimen. Wood contains water, so the structure you see might be altered by vacuum dessication. The vacuum can also have the effect of sucking other material out from the interior of the sample: the blob visible centre-right in Fig. 2 might be resin that has been sucked out of the wood in this way.
It seems to have been in the 1980s that someone first had the idea of putting a violin in a medical scanner, to reveal a different kind of “hidden detail”: see for example the article by John Waddle and Steven Sirr . Medical scanners use x-rays and rely on a processing method called “computed tomography”, so they are often known as “CT scanners”. A CT scan can reveal many things: detailed shape and thickness information, and also things like woodworm damage and old repair work.
CT scans formed part of the ambitious “Strad3D project”, in which three famous old violins were subjected to every kind of test and measurement that was available in 2006. All the results can be seen on this web site. Figure 4 shows the three violins stacked up and entering the CT scanner. Access to scanner time was still at a premium in those days, hence the combined scan of three instruments at once. You can see a video of the resulting scan here: go to the option “Three violins axial compare”.
In the years since then, the technology has progressed in leaps and bounds. Medical CT scanners are optimised for the particular business of imaging the human body, but laboratory-based scanners have been developed that are targeted at tasks like non-destructive testing of engineering components. These can have significantly higher resolution than medical scanners, and the processing software has also been developed differently to allow non-medical aspects of behaviour to be examined. The result is that some stunning images of musical instruments are now available. Figure 5 shows a screen shot from this YouTube video, showing a “deconstructed” Stradivari violin.
You can see many interesting details by studying Fig. 5. You can see individual annual rings in the wood of the top, the back and the bass bar. This shows how Stradivari chose and cut his wood. You can see the soundpost (leaning at a slightly unexpected angle, presumably deliberate). On the underneath of the top plate, around the end of the soundpost, you can see a reinforcing patch put in at some stage by a restorer. In the lower left, you see the label in the instrument – but the one thing the CT scan does not see is the writing on it!
Figure 6 shows something else that can be extracted from the high resolution CT scan data. It shows a thickness map of the back plate of the violin, something violin makers are always very interested in. Makers are also very interested in the arching shape of the top and back plates. It used to be common for violin makers to have in their workshops plaster casts of famous violins like the one shown here. But these days, they may have 3D-printed replicas of plates made from CT scan data.
What are the snags that can cause misleading results in a CT scan? The main thing is that x-rays aren’t very good with metal. If you watched the video from the Strad3D project, you may have noticed vigorous “starburst” flashes at certain points: these occurred where the viewing section passed through metal objects like the fine-tuners attached to the tailpiece in order to tune the top string.
A more subtle issue to be aware of in the back of your mind is that the images you see are not a direct result of observation: they are reconstructed from the raw data by sophisticated computer software. The programmer of that software has made some choices, which influence what you see. As a simple example, the colour in Fig. 5 is created by software. It has nothing directly to do with the actual colour of the wood, it has been chosen for good visual effect (very much like those famous images from the Space Telescope). More detail of the procedure can be found in an article by Rudolf Hopfner .
There is another piece of equipment originally developed for non-destructive testing, which has been applied to musical instruments. The method is called pulse reflectometry, and it is useful for long, thin structures like pipelines or cables. With a pipeline, for example, you send a pulse of vibration or sound into the wall of the pipe, or through the fluid contained within the pipe, and you record the reflections that come back. By analysing the pattern, you can detect things like blockages, corrosion or breaks in the pipeline. That can tell you what has gone wrong, and also where you need to dig the road up to repair the damage.
This method has been applied to the rather different problem of reconstructing the bore profile of musical wind instruments. The bore profile is the most important thing to know about a wind instrument, either for the purposes of making a replica of a historic instrument or for understanding the acoustical behaviour of an instrument. A measurement of the bore profile can also shed light on possible internal faults such as leaky valves in brass instrument.
We can get an idea of how the method works by a hand-waving argument. Suppose first that we have a cylindrical pipe with an abrupt change in cross-sectional area, like the sketch in Fig. 7. Now suppose that a pulse of acoustic pressure is sent into the pipe at the left-hand end. We will assume that it is a plane wave, with constant pressure across any particular cross-section of the pipe. When this pulse reaches the jump in cross-section, a reflected pulse will be generated which will travel back down the pipe. There will also be a transmitted pulse, which carries on into the second section of the pipe.
We can learn three things by observing the reflected pulse, with a microphone near the left-hand end where the original pulse was sent in. The time delay between the original pulse and the reflected pulse tells us how far down the pipe the jump in section occurred. The amplitude of the reflected pulse can be used to work out the ratio of the two cross-sectional areas at the jump, using a standard piece of textbook theory. Finally, the sign of the reflected pulse tells us whether the cross section jumped to a larger or a smaller value than the original pipe: if there is a reduction of area, the reflected pressure pulse has the same sign as the original pulse, but if there is an increase in area the reflected pulse will be inverted. Putting these three things together, we have full information about the jump in cross-section.
Now for the hand-waving part. In a musical instrument, the bore might have jumps at some positions, but it will also have continuous changes along its length. Well, we can imagine approximating any bore profile by a kind of staircase profile, with small jumps separated by short sections of parallel pipe. Each of those small jumps will generate a reflection which can be analysed as I have just described. So with a bit of effort in the computer software, we should be able to reconstruct the entire bore profile. Needless to say, there are details of this processing that need to be thought about very carefully: see for example the discussion by Sharp and Campbell .
But the process can indeed be made to work reliably, and we can show an example. Figure 8 shows the experimental setup. A trumpet is being tested. The input acoustic wave is generated by a loudspeaker, controlled by a computer. This is connected to the trumpet via a long length of tube with a constant cross-section. The tube is coiled up in the picture: the sound waves inside the tube do not care about gentle curves, a fact which is equally relevant to the trumpet itself. The bore profile that will be reconstructed is “unwound”.
Somewhere in the middle of the long tube, a microphone is placed to observe the incoming sound pulse and also the reflected sound returning from the trumpet. The reason for this long tube is to minimise the influence of possible complicating factors. For example, the reflected wave from the trumpet will travel back down the tube past the microphone, and then when it reaches the loudspeaker it will be reflected back into the tube. The tube between the microphone and the loudspeaker needs to be long enough that this next reflection is not confused with the reflected wave from the trumpet, which we are trying to measure as accurately as possible.
Figure 9 shows two reconstructed bore profiles of a trumpet. The red curve describes the shape when no valves are depressed, so that the total length of the tube is as short as possible. The blue curve shows the result of depressing all the valves, to give the longest combined length of tube. The profile is expressed in terms of an effective radius, on the assumption that the cross-section is always circular. This will not be entirely true in practice, but it makes no difference to the validity of this measurement provided any local perturbations to the cross-sectional shape are small compared to the wavelengths of sound that we are interested in. Wiggles can be seen, especially in the blue curve, marking positions where the details of the valve mechanisms make small changes to the effective cross-section. Figure 10 shows a 3D rendering of the bore profile from the blue curve in Fig. 9. In both Figs. 9 and 10, the flaring bell of the trumpet is not shown out to its actual total radius: the assumptions behind the reconstruction process start to break down when the flare becomes too rapid, so the results are less accurate.
 John R. Waddle and Steven A. Sirr, “X-ray computerized transaxial tomographic analysis of stringed instruments”, Catgut Acoustical Society Journal (series II), 3, 2, 3—8 (1996).
 Rudolf Hopfner, “Hi-res revelations”, The Strad 129, 1533, 54—59 (January 2018).
 David B. Sharp and D. Murray Campbell, “Leak detection in pipes using acoustic pulse reflectometry”, Acta Acustica united with Acustica 83, 560–566 (1997).