What Type of Wood is My Violin Made From 2

Finding the Volume of Ebony Parts The weight of the parts of the violin not made of the specific wood being investigated is necessary to find out, as this weight needs to be removed from the violin’s overall weight, in order to compare the weight of the specific wood with the modelled volume and find the density. The volume must therefore be found first, and the weight can then be found by using the wood density of that wood - in this case, ebony. There are four tuning pegs on the violin (one per string) made of ebony, which I have modelled using an elliptical cylinder for the handle and a frustum for the taper end (see Figure Two). The formula for the area of an ellipse 14 is: Area = (cross-length a x cross-length b)π As the ellipse is a similar shape - though not exactly the same - as the handle, finding the area and depth of the peg (of 0.4cm, using Figure Two dimensions) enabled me to find the volume: 2.3 x 1.1 x π = 7.948cm2 7.948 x 0.4cm = 3.179cm3 I decided to use a frustum to model the tapered end of the peg, as it a cylinder does not reflect the changes in width from the top to the bottom (Figure Two). The volume for a frustum 15 is: V = (h ÷ 3)(upper plane area 2 + lower plane area 2 + (upper plane area)(lower plane area)) Therefore, I needed to work out the area of the upper plane (finding a circle): Area = πr2 = π(0.7 ÷ 2)2 = π(0.35)2 = π(0.35)2 = 0.1225π = 0.3848cm2 I followed the same method to find the area of the lower plane (area of a circle): π(1.1 ÷ 2)2 = π(0.55)2 π(0.55)2 = 0.3025π = 0.9503cm2 Next, I substituted these values back into the formula (above) to find the volume: (h ÷ 3)(0.38482 + 0.95032 + (0.3848 x 0.9503) = (4÷ 3)(1.417) = 1.889cm3 Therefore, the volume for each peg would be the sum of the elliptical cylinder and the frustum volumes, and for the volume of all four pegs, the sum would have to be multiplied by 4: 3.179 + 1.889 = 5.068cm3 per peg 5.068 x 4 pegs = 20.27cm3 The end button (Figure One) is a very small part of the violin shaped like a hemisphere. The volume of a sphere16 is shown by the formula: V = (4 ÷ 3)πr3 I then substituted the endpin’s dimensions (Figure Two) into this formula: (4 ÷ 3)π(1.5 ÷2)2 = (4 ÷ 3)π(0.5625) = 2.356cm3 I then halved the answer to find the area of the endpin’s ebony hemisphere: 2.356 ÷ 2 = 1.178cm3 The fingerboard of the violin (see Figure One) is made of ebony, and shaped like a trapezoid. The formula for the area of a trapezium 17 is: A = (h ÷ 2)(side a + side b) Using this, I substituted in the dimensions of the fingerboard (Figure Seven), and multiplied it by the depth to find its volume: (h ÷ 2)(4.1+2.4) = (27.1 ÷ 2)(6.5) = 88.08cm2 88.08 x 0.5 = 44.04cm3 2.4cm Figure Seven: the dimensions of the fingerboard 27.1cm 0.5cm 4.1cm Therefore, the sum of the ebony parts (pegs, endpin and fingerboard) is as follows, and this can be used to find their weight: 20.27 + 1.178 + 44.04 = 61.08cm3 Finding the Weight of Ebony Parts With the volume established, I used information from several sources on the internet to find the wood density of ebony. However, the values given differed depending on the website, and websites gave values for more than one type of ebony. This data is displayed below in Table One, with six samples of different websites and types. Ebony type A18 B19 C20 D21 E22 F23 Density (g/cm3) 0.9600 1.1200 1.100 1.300 0.9780 0.7680 Table One: different types of ebony and their densities. Because I do not know the type of ebony used in my violin, I decided to take an average of the different values I found, and use that as the density I would use to find the weight of the ebony: 0.9600 + 1.1200 + 1.100 + 1.300 + 0.9780 + 0.7680 = 6.226g/cm 3 6.226 ÷ 6 = 1.038g/cm3 Using this value, I was able to find the weight of the ebony parts using the formula below and substituting in the values I had found: Volume x density = weight = 61.08cm3 x 1.038g/cm3 = 65.49g Finding the Weight of Additional Parts Other parts of the violin were not as simple to model. I removed the chinrest (Figure One) altogether, so it was not included in the weight or the modelling, but I could not remove the tailpiece, strings or bridge. As they are difficult to model due to irregular shapes (see Figure One), I looked them up on the internet and found values for their item weight on the Amazon website. Because the three items are generic, and do not usually differ between violins, the weights I found are likely to be accurate. They are displayed in Table Two below. Item Tailpiece24 Strings25 Bridge26 Weight (g) 18.10 40.80 4.540 Table Two: different components of the violin and their weights, as listed on Amazon. In order to add these values to the weight of the ebony, the total of these additional parts is shown below: 18.10 + 40.80 + 4.540 = 63.44g Calculating the Wood Density and Species In order to calculate the wood density, I first measured the weight of the whole violin, using an electronic kitchen scales. This only gave a value to 3sf (as it did not give decimal places), however I considered this value - 361g - accurate enough to incorporate into the density equation. I then had to find the weight of the other parts of the violin I wasn’t interested in finding the density of - the ebony parts I modelled, and the additional parts the weights of which I found online. I subtracted this value from the total measured weight to give the weight of the wood remaining: Measured weight - (ebony parts + researched parts) = wood weight = 361 - (65.49 + 63.44) = 431 - 128.9 = 232.1g From this, I could incorporate the value I found for the volume of the modelled wood into the formula for density, therefore finding the wood density of the desired species: Weight ÷ volume = density = 232.1 ÷ 354.34 = 0.6550g/cm3 Finally, I had to relate this value back to individual species of wood I had found online. The body wood of the violin, as mentioned previously, is generally made of spruce. This prompted me to search the internet for different values of spruce wood density. I found several different values from different sites, again differing between spruce type. These values are displayed below in Table Three. Spruce type Red27 Black28 Norwegian29 White30 Sitka31 Density (g/cm3) 0.4130 0.4280 0.4300 0.4310 0.4500 Table Three: different types of spruce and their densities. In addition to these specific values, I found that spruce density 32 can range from 0.4g/cm 3 to 3 0.7g/cm , meaning that my value of 0.6550g/cm3 was not out of the limit for spruce. This suggests that the violin is made of Sitka spruce as it is closest to the Sitka’s density than any other type of spruce, at 0.4500g/cm3. However, the difference between even the lowest density for spruce (Red 0.4100g/cm3) and Sitka spruce is smaller than the difference between Sitka spruce and my value. This suggests that the wood is of a different species, or the wood has been aged or treated to increase the density of the wood. However, this will be explored further in the evaluation. Because the data is not explicit in regards to specific wood species, the wood type cannot be used as the only reason behind the loudness of my violin compared to others. Also, because I did not follow this process with other violins, I cannot determine that there is a difference between the density of the wood in different violins. Despite this, given the lower densities of different types of spruce used to make violins compared to my violin’s, I can argue that the higher the density of spruce, the louder the violin is. In any case, I have been able to learn a lot about my violin and about integration, modelling 3D shapes and calculating density. Evaluation This final calculation may be inaccurate because of two factors. Firstly, my modelling of parts which gave volumes (for both the desired wood and the other parts made of ebony) could have given an incorrect values for the weight of the wood from which the density was calculated. Secondly, the entire premise my calculation was based on could have been inaccurate. These will be explored in more detail below. My modelling could have been inaccurate for a number of reasons. One reason is that the body of the violin - the most significant part of the wood volume of used in the density equation could have different thickness throughout. I assumed a universal thickness of 0.2cm, but due to the curved nature of the violin and the support required on either end, this is probably the lowest value. I had come to the value of 0.2cm by measuring at the centre of the instrument, through the f-holes (Figure One), so the wood was likely thinnest there. Additionally, translating each graph down by 0.2cm does not give a thickness of 0.2 all the way round a parabola, just for the turning point of the graph - this will make the density appear higher than it is in reality. In regards to f-holes, the volume of these f-shaped gaps was not considered when calculating the volume of the body. A component of the violin not shown in Figure One is the heel - on the back, where the body meets the neck. This has been omitted from the calculations for the spruce wood, so the total is wrong. Likewise, the soundpost and ribs - internal parts of the violin and impossible to measure from the outside - have been omitted. Also, as the scroll was modelled using cones rather than its own unique shape, this estimation is inaccurate. The neck of the violin - modelled as a half-cylinder - is actually shaped more like a halffrustum, as the top is narrower than the bottom. Due to this taper, the modelling is incorrect. Similarly, the head of the peg - which I used an elliptical cylinder to model - is not perfectly elliptical, nor flat on the sides, which makes the volume calculations for ebony inaccurate as well. Again, the fingerboard is not flat - it is curved, which changes the volume again as the model is incorrect. The ebony values have another variable - the density I used to find the weight was a mean estimate of different types, meaning this is likely to be inaccurate, making the weight subtracted from the measurement of the violin’s total weight also inaccurate. Other problems with measurement and modelling concern decimal places - as I rounded to 4 significant throughout, some values were slightly inaccurate. However, because the degree of difference was so small, this is insignificant in the final result and is unlikely to have altered the final value. Another issue is the values I found on the internet - because these were not from my violin, it is impossible to know if their weights are applicable to my violin. Additionally, the weights could have been inaccurate, as there is no real reason for the item weight to be accurate to the gram (or to two decimal places of the gram, in the case of the bridge). The values for the wood type could also be irrelevant: during the violin-making process, the wood may have gone through processes like dyeing, fermenting, ageing etc. which could change the density of the wood. This would invalidate all the values found on the internet, as the wood would have been altered to make it suitable for a violin. However, there could be another reason for the inaccuracy - the whole idea this IA is based on could be wrong. As mentioned in the introduction, there are many different reasons why a violin sounds the way it does - the assumption that, in my violin, it is the type of wood that affects the loudness could be incorrect, or at least misguided. My bow (pulled across the strings to produce a sound) changed when I bought the violin being investigated, so this could be the cause of the relative loudness. Other factors could be the bridge structure, the tension and quality of the strings, abd the size and quality of the soundpost necessary for creating audible sounds. Alternatively, the loudness could have something to do with wood, but perhaps not the species. The quality of wood and its treatment could affect the quality and sound of the whole instrument, making it louder than others. Also, tradition and some sources argue that the more a violin is played, and the older it is, the better the quality - in this case, the loudness is. To conclude, I have found many inaccuracies in my method, but the complex shape of an instrument such as a violin is difficult to model, as each instrument differs and the component parts are hidden, irregularly-shaped or have many curves (making integrating the area difficult). To improve, I could have done different models of the same component using different methods, and compared them.