QUESTION: How does the tension of the viola and violin relate to the frequency of the four strings being tested? We are also going to compare the thickness of the string and see if it makes a difference when both are tuned (stretched with weights) to the correct pitch of an 'A' and 'G' string.
HYPOTHESIS: We think the strings of different thickness and same octave [example: the violin A string vs. the viola A string] will have different frequencies when weights with equal tension are pulled on the strings. We decided to experiment with the 'G' string and find out if it also makes a dramatic differences within the two. We believe that when the string is plucked, the strings with thicker widths will vibrate less, thus making the string have less frequency--whereas thinner string will have higher frequency due to its width.
BACKGROUND INFORMATION: We are very fortunate to know Roger Rolind, a string instrument maker. He owns his own violin shop downtown Atlanta, and is also an acquantence of mine. Questioning him about the differences in sound and tension of string instruments was easy as pie--well, almost. (It took us a second visit to clear up further information). We found out that different strings each gave off a specific color in sound (tambre) and frequency due to it's different thickness and brand of string.
Strings in the medieval times were originally made of cat or cow guts that were dried and wound up into a thin string; called Plain gut. Plain gut strings are still present today for acoustic instruments but are not used normally. They made different sounds due to the natural hard thickness and dried texture of the strings. Thicker strings vibrated less than thinner strings. Today, most string companies make strings made out of aluminum or steel. We decided to test on Helicore Strings, which are made of nylon for easy stretch, and wrapped with aluminum for strength. Helicore string are popular with many of its users because the quality is worth the money. The different sounds that different strings give out is most likely due to the different materials it is made out of. Different material textures can also lead to different thicknesses, which can give off different tonal qualities.
We decided to pluck the strings when collecting our data and sound, instead of bowing it with the bow, because plucking is more consistent than bowing. If bowed, we would have to measure how much bow we would have to use and decide how much rosin would be needed. Rosin is a sticky powder that helps the bow grip onto the strings, so when playing, the bow will not slide everywhere.
MATERIALS:
1. Two violin A and G Helicore strings (extra one in case of breakage during testing procedure)
2. Two viola A and G Helicore strings
3. Sonometer (device in which strings will be mathematically weighed and tested for tension)
4. Micrometer (device which digitally measures the width of each string)
5. Universal Lab Interface (computer program which will measure the frequency of string when plucked)
6. One ULI Microphone
7. The Physics of the Violin book by, Lothar Cremer, translated by John S. Allen
8. The Physics textbook
9. Electronic fine tuner
10. Graph Analyzer
PROCEDURE:
1. We had to gather materials. We got four A strings and four G strings (two of each for both instruments) from Roger Rolind, the violin maker. We had all of them measured with the micrometer and recorded the measurements.
2. Set up the computer for analyzing and testing the frequencies on each string. (Set up the Universal Lab Interface and connect the probes to be used).
3. Set up the Sonometer and attach strings to the box.
4. Gather different weights to use on the sonometer.
4a. Tune strings to correct pitch by using the Fine Tuner.
5. Use the ULI microphone to double-check the frequency and pitch of the string.
6. Record the information the computer program gives about each string.
7. Repeat steps five and six, 10 times for each string
8. Record all data and insert information into the data tables.
9. In the meantime, have one person surf the web for pictures of violins/violas, and any links we might want to mention in our web page.
10. Have other person open up Graph Analyzer and insert all data to calculate and figure out the standard deviation and other averages.
DATA:
A string for the violin (Width is 0.65 mm)
Number of Trials | Frequency (Hz) | Amplitude |
1 | 455 | 4.8 |
2 | 455 | 2.6 |
3 | 412-455 | 3.9 |
4 | 412-455 | 1.3 |
5 | 412-455 | 1.3 |
6 | 390-477 | 3.8 |
7 | 1279-1322 | 3.5 |
8 | 390-477 | 1.8 |
9 | 1279-1322 | 3.5 |
10 | 412-455 | 1.6 |
A string for the viola (Width is 0.62 mm)
Number of Trials | Frequency (Hz) | Amplitude |
1 | 412-455 | 1.9 |
2 | 412-455 | 3.5 |
3 | 412-455 | 3.0 |
4 | 412-455 | 2.8 |
5 | 412-455 | 3.5 |
6 | 412-455 | 3.2 |
7 | 412-455 | 5.5 |
8 | 412-455 | 5.6 |
9 | 412-455 | 4.8 |
10 | 412-455 | 3.2 |
G string for the violin (Width is 0.77 mm)
Number of Trials | Frequency (Hz) | Amplitude |
1 | 369-412 | 1.4 |
2 | 369-412 | 1.8 |
3 | 1322-1366 | 1.2 |
4 | 1322-1366 | 2.8 |
5 | 369-412 | 1.5 |
6 | 1322-1366 | 2.1 |
7 | 369-412 | 1.6 |
8 | 369-412 | 1.3 |
9 | 369-412 | 2.0 |
10 | 1322-1366 | 2.0 |
G string for the viola (Width is 0.71 mm)
Number of Trials | Frequency (Hz) | Amplitude |
1 | 1192-1236 | 1.8 |
2 | 1149-1192 | 1.5 |
3 | 1149-1192 | 1.2 |
4 | 1149-1192 | 2.2 |
5 | 1149-1192 | 1.8 |
6 | 1149-1192 | 1.1 |
7 | 1149-1192 | 1.4 |
8 | 1106-1149 | 1.9 |
9 | 1149-1192 | 2.2 |
10 | 1106-1149 | 1.9 |
WEIGHTS
| Violin A | Viola A | Violin G | Viola G |
20 g | 80 g | 40 g | 50 g |
50 g | 300 g | 50 g | 20 g |
200 g | 0.5 K | 200 g | 100 g |
1 K | 2 K | 50 g | 1 K |
2 K | 2 K | 20 g | 1 K |
1 K | 0.98 K | 3 K | 0.5 K |
0.98 K | 0.5 K | 0.98 K | 0.98 K |
TOTAL: 5250 g | TOTAL: 6360 g | TOTAL: 4340 g | TOTAL: 3650 g |
ANALYSIS
AVERAGE OF AMPLITUDE:
| Violin A | Viola A | Violin G | Viola G |
| Standard Deviation: 64.3 | Standard Deviation: 1.21 | Standard Deviation: 0.479 | Standard Deviation: 0.386 |
| Minimum: 1.30 | Minimum: 1.90 | Minimum:1.20 | Minimum: 1.10 |
| Maximum: 2.06 | Maximum: 5.60 | Maximum: 2.80 | Maximum: 2.20 |
| Mean: 23.1 | Mean: 3.70 | Mean: 1.77 | Mean: 1.70 |
AVERAGE OF HERTZ (Hz)
| Violin A | Viola A | Violin G | Viola G |
| Standard Deviation: 371 | Standard Deviation: 22.1 | Standard Deviation: 480 | Standard Deviation: 32.5 |
| Minimum: 390 | Minimum: 412 | Minimum: 369 | Minimum: 1.11e+03 |
| Maximum: 1.32e+03 | Maximum: 455 | Maximum: 1.37e+03 | Maximum: 1.24e+03 |
| Mean: 629 | Mean: 434 | Mean: 772 | Mean: 1.17e+03 |
We analyzed data by collecting our data and comparing the amount of weights needed to match with the correct pitch, which later lead to its frequency. With the exception of the A Viola String, our data wasn't very accurate. After we collected our data, we found that the frequency figures collected should have all been in the hundred place--not in the thousand place. Having that knowledge in mind, we could've done more trials to make our data more consistant. Although our data wasn't very accurate, it was very consistant. We always got the same repeated frequency, as we discovered the A Viola String had maintained its same frequency throughout all the trials. Factors that affected our experiment included the collection of outside noises and interferences which the microphone picked up.
CONCLUSION
We believe as a team, this experiment went successfully. The topic we chose was rather a complicated one (i.e. when talking about outside variables, understanding a string instrument). However, at the same time, the basic concepts of physics was pretty easy to understand, as it dealt with frequency and wavelengths. Initially, we wanted to find out if the width of the string really made a big deal with the tambre or the frequency. We also wondered if the number of weights really made a difference in the wavelenghths and the vibrations each string had. The Viola strings are naturally thicker, probably because the viola is bigger than the violin. It was interesting to see that the A strings needed much more weight and tension than the G strings. We concluded that this was due to the tightness and high pitch sounds that A string gave off, opposed to the loose, more mellow sound the G string gave off. The G string had less frequency than the A string. We can probably relate this to what Roger Rolind, violin maker said, when mentioning that thinner strings with a more high pitch makes more vibrations than strings that have less weight/tension. We found that the violin G vibrated 480 times a second when plucked, whereas a viola G vibrated 32.5 times per second. We can definately see the incredible difference in the two strings. When comparing this to the weights, the viola G string had 690 grams less than the violin G string. So, we assumed that the weights had to do something with the tension and the amount of vibrations per second. However, when looking at the viola A string, it had 1110 grams more than the violin A string. This was really interesting because when we compared it to the frequency, we found that the violin A had 371 vibrations per second, whereas the violin G had a low 22.1 vibrations per second. The weights seem to be significant when dealing with the lower sounding string, such as the G string, but when tested with strings which were thinner (i.e. A strings), it had the opposite results. We can make this assumption where thickness does make a difference, because the viola A string was thinnner that the violin A. (viola-0.62 mm vs. violin-0.65 mm). When discussing outside variables, the structure of a string instrument really makes a difference in how the tambre of each string will give out. Another factor is when the string is plucked, rather than bowed. Plucking the string gives us a trial free from oscillations. Another factor can be the brand of string and how flexible a string can be.Walter
Special thanks: Physics Dept., GSU, Atlanta; GSU Music Dept., Atlanta; WSB Radio, Atlanta.
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