{"id":4998,"date":"2015-05-13T23:28:54","date_gmt":"2015-05-14T03:28:54","guid":{"rendered":"http:\/\/pages.vassar.edu\/magnes\/?p=4998"},"modified":"2015-05-13T23:28:54","modified_gmt":"2015-05-14T03:28:54","slug":"greg-and-ted-guitar-and-piano-string-conclusion","status":"publish","type":"post","link":"https:\/\/pages.vassar.edu\/magnes\/2015\/05\/13\/greg-and-ted-guitar-and-piano-string-conclusion\/","title":{"rendered":"Greg and Ted Guitar and Piano String Conclusion"},"content":{"rendered":"

Introduction<\/span><\/b><\/p>\n

Our initial plans for this project were to model and guitar string, piano string, and drum head in MatLab, then compare data calculated to a real scenario, using the physical instruments and recording the sounds they create. \u00a0We were able to complete the guitar and piano strings, but were not able to advance to the drum head due to time constraints. \u00a0However, we did get a lot of good data from our experiments with the guitar and piano strings.<\/p>\n

Guitar String<\/span><\/b><\/p>\n

For this part of our project, we modeled a guitar’s B string in MatLab, and plucked the string at different points: once at the midpoint of the string, once 1\/5 the string length\u00a0from the bridge, and once 1\/20 the string length from the bridge. \u00a0In the proceeding images, you can see the string oscillations, the force of the string on the guitar bridge with respect to time, and the Fourier Transform of these force graphs, which reveal the frequencies inside.<\/p>\n

Modeled Guitar Data:<\/span><\/p>\n

\"Modeled<\/a><\/p>\n

Frequencies of waveforms (Fourier Transform):<\/span><\/p>\n

\"Modeled<\/a><\/p>\n

The force of the string on the bridge with respect to time is nearly\u00a0identical to the sound wave that the string produces in the atmosphere, thus we were able to use that data to find the frequencies in our calculated string. \u00a0We also shifted the frequencies on the graph of the Fourier Transform for visual purposes (if not shifted, they would line up on top of each other and be difficult to distinguish).<\/p>\n

Next, we recorded a guitar B string, identical to the one we modeled, and Fourier transformed those recordings to obtain the frequencies inside.<\/p>\n

Frequencies of Physical Guitar String:<\/span><\/p>\n

\"RealGuitar\"<\/a><\/p>\n

Here are the recorded guitar sound files. \u00a0Note as the pluck gets closer to the bridge, the tone of the guitar becomes harsher. \u00a0We will discuss this soon.<\/p>\n

String Plucked at (1\/2) distance:<\/span><\/p>\nhttp:\/\/pages.vassar.edu\/magnes\/files\/2015\/05\/midpluck.wav<\/a><\/audio>\n

String Plucked at (1\/5) distance:<\/span><\/p>\nhttp:\/\/pages.vassar.edu\/magnes\/files\/2015\/05\/fifth-pluck.wav<\/a><\/audio>\n

String plucked at (1\/20) distance:<\/span><\/p>\nhttp:\/\/pages.vassar.edu\/magnes\/files\/2015\/05\/20thpluck.wav<\/a><\/audio>\n

In our code for the modeled guitar string, the calculated waveform is played for the viewer, and as seen from the physical guitar, the tone of the sound gets harsher as the pluck gets closer to the bridge. \u00a0This harsher sound is the stronger presence of the overtones in the waveform as seen in our Fourier transforms. \u00a0As the pluck gets closer to the bridge, strength of the higher frequencies increases, which is why the sounds produced becomes\u00a0much harsher. \u00a0This is what we expected and found with this part of the experiment. \u00a0Comparing our Fourier transform graphs, we see that the peaks at the higher frequencies increase with each pluck\u00a0closer to the bridge. \u00a0We can also see that the closer the pluck is to the bridge, the lower the fundamental frequency becomes present in the produced sound.<\/p>\n

However, there are\u00a0some inconsistencies between the modeled and physical strings. \u00a0The modeled string did not contain and decaying properties, where the physical string did. \u00a0Also, the modeled string data was calculated using two dimensions when the physicals string would utilize all 3. \u00a0 This important difference shows in the Fourier Transform of the modeled string. \u00a0When the modeled string is plucked at the halfway point, every other frequency (or peak) is eliminated from the Fourier transform; same as when plucked at 1\/5, the fifth and tenth peak is eliminated. \u00a0In this modeled state, we are effectively killing these overtones by plucking where they would naturally occur on the string. \u00a0The decay properties of the physical string allow these “ghosted” frequencies to sound because the string can move freely rather than stay in a fixed 2-D dimension and fixed wave profile. \u00a0Another reason behind this, could be that the physical string is not of ideal form, meaning it is a series of coiled wires rather than a solid string. \u00a0This could have imperfections giving rise to these “ghosted” frequencies.<\/p>\n

Another small discrepancy in our data is that the fundamental frequency of the physical string plucked at the halfway point is lower than when plucked at the other distances. \u00a0We don’t see this in our modeled system because the amplitude of the pluck was held constant for each pluck (giving us the results we expect). \u00a0On the physical string, the string is able to bend more at the middle than closer to the bridge. \u00a0Thus to get an equal volume\u00a0pluck, we must do a harder pluck in the middle than closer to the bridge. \u00a0If we kept the amplitude of the plucks for the physical guitar the same, we would expected the\u00a0power of the individual frequencies to closer match the modeled ones.<\/p>\n

Piano String<\/span><\/strong><\/p>\n

For this part of our project, we modeled a piano’s middle C\u00a0string in MatLab, and struck\u00a0the string with different forces: Once softly, and once more powerfully. \u00a0In the proceeding images, you can see the string oscillations, the force of the string on the piano\u00a0bridge with respect to time, and the Fourier Transform of these force graphs, which reveal the frequencies inside, all for two different hit intensities.<\/p>\n

The model included a hammer with mass and an original velocity (which changes between the two trials) as well as a felt on the hammer which behaves as a spring. Here the compression of the felt is dependent on the position of the hammer and the string section where the\u00a0hammer strikes, and which affects the positions of the freely moving hammer and string based on its compression. When the compression changes signs, we know that the hammer has left the string and we automatically give the string no outside force.<\/p>\n

Modeled Piano Data and Frequencies<\/span><\/p>\n

\"Screen<\/a><\/p>\n

The force of the string on the bridge with respect to time is nearly\u00a0identical to the sound wave that the string produces in the atmosphere, thus we were able to use that data to find the frequencies in our calculated string.<\/p>\n

Next, we recorded a piano C\u00a0string, identical to the one we modeled, and Fourier transformed those recordings to obtain the frequencies inside.<\/p>\n

 <\/p>\n

Frequencies of Real Piano String<\/span><\/p>\n

\"RealPiano\"<\/a><\/p>\n

 <\/p>\n

Here are the recorded piano\u00a0sound files. \u00a0Note when the strike is harder, the tone of the guitar becomes harsher. \u00a0We will discuss this soon.<\/p>\n

 <\/p>\n

Hard String Hit:<\/span><\/p>\nhttp:\/\/pages.vassar.edu\/magnes\/files\/2015\/05\/hardmiddleC.wav<\/a><\/audio>\n

Soft String Hit:<\/span><\/p>\nhttp:\/\/pages.vassar.edu\/magnes\/files\/2015\/05\/softmiddleC.wav<\/a><\/audio>\n

 <\/p>\n

In our code for the modeled piano\u00a0string, as the strike\u00a0gets harder, strength of the higher frequencies increases, which is why the sounds produced becomes\u00a0much harsher. \u00a0This is what we expected and found with our simulations. \u00a0A similar trend was also found in the Fourier transformed recorded sound files.<\/p>\n

However, there are\u00a0some inconsistencies between the modeled and physical strings. One such difference was the lower fundamental frequency than the second overtone in the recordings, as compared to our model. This could be due to the amplifying qualities of the piano box. The modeled string did not contain and decaying properties, where the physical string did. \u00a0Also, the modeled string data was calculated using two dimensions when the physicals string would utilize all 3. \u00a0The model we simulated made assumptions about the spring like qualities of the felt, the width of the hammer, as well as the strike intensity, which we couldn’t make equivalent to the recorded strikes. This created some strange differences, including a strangely sharp hammer hit (not as soft as one might expect from a spring, as well as differing from the textbook’s predicted hammer\u00a0behavior). We brainstormed what may be it’s cause (the hammer velocity, the original felt thickness, the hammer’s strike position) but couldn’t find a solution.<\/p>\n

Conclusion<\/strong><\/span><\/p>\n

In conclusion our results were what we expected with some degree of uncertainty. String plucks closer to the bridge and harder string strikes produce more overtone notes relative to the fundamental frequency.\u00a0If we had more time\/if this project were to continue further, we would explore the addition of a damping coefficient in our modeled experiments and compare with physical strings, investigating the discrepancies mentioned earlier. \u00a0We would also begin to explore the drum head dynamics, experimenting with two 3-D membranes, connected through a closed hoop, similar to the structure of an actual drum.<\/p>\n

The following link is to a google drive containing all of our code and sound files.<\/p>\n

https:\/\/drive.google.com\/folderview?id=0ByhnW_B9B6q9flE5bWtTal9Yd19ZYzhrOGpUbjctMUhIM3FMRGxvMDVMZkF3NUJSbFJ1MEU&usp=sharing<\/a><\/p>\n

Please note, if you are planning to run the code that involves the recordings of the instruments, YOU MUST CHANGE THE DIRECTORY IN WHICH THE CODE CALLS THE SOUND FILE. \u00a0Each space in the code is noted where this part should be edited. \u00a0This needs to be done as the naming of folders and drives varies from computer to computer. \u00a0Not only must the correct location of the file be used, but the sound files must be saved in the same location as the MatLab code or it will not run. \u00a0Also the correct sound file must be called in each spot, or the sampling will be off\/ the code will not run properly.<\/p>\n","protected":false},"excerpt":{"rendered":"

Introduction Our initial plans for this project were to model and guitar string, piano string, and drum head in MatLab, then compare data calculated to a real scenario, using the physical instruments and recording the sounds they create. \u00a0We were able to complete the guitar and piano strings, but were not able to advance to […]<\/p>\n","protected":false},"author":2594,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4998","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/4998","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/users\/2594"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/comments?post=4998"}],"version-history":[{"count":2,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/4998\/revisions"}],"predecessor-version":[{"id":5063,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/4998\/revisions\/5063"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/media?parent=4998"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/categories?post=4998"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/tags?post=4998"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}