# AiS Challenge Team Interim

Team Number: 49

School Name: Manzano High School

Area of Science: Physics

Project Title: Frequencies & Aging of Guitar Strings

Our group has learned many important skills required for success in the Adventures in Supercomputing Challenge. Ever since the first day of class, our instructor has been teaching us the necessary aspects that are required in the curriculum.

First, we spent six weeks learning the general aspects of html. We learned about hyper links, placing images on a web page, placing colors, and cutting and pasting. Our final project in that rubric was to create our very own web page consisting of pictures, html codes, and placing tables. We edited an existing web page by replacing it with our own files and folders.

Then, we spent two to three weeks setting up both MHS AiS Challenge Linux accounts and accessing our New Mexico AiS Challenge Unix accounts. In our local Linux domain, we learned numerous Unix commands such as, ls, cd, mkdir, rmdir, making files via "pico", and copying/moving files. We also set up both telnet and ftp software at our home computers to allow us to interact with both MHS and the AiS Challenge site.

We spent a week discussing general math algorithms for computing geometric shapes and computing distances and velocities in simple motion problems.

Next, we spent five weeks learning the basic concepts of C++ programming code. We learned concepts and programming skills such as setting up the main function, cout and cin commands, mathematical computations, for loops, the use of if-else, mod, and setting up arrays. Also, we used the math algorithms in a Unix machine as the basis of most of our programs. We combined the math algorithms with programming skills towards computing the volume and surface area of a sphere and solving physics problems of motion. We programmed over ten programs that compute different kinds of problems. Basically, our instructor provided us with ample information to write the program code for our project.

### Problem Statement Regarding Frequencies of Vibrating Strings

The problem that our group is attempting to solve is to help people who play the guitar to know when their guitar string is old. Our group is going to test the harmonics of old and new strings of two basic string materials (i.e. nylon, steel). Our project is important because it will hopefully show the life of a guitar string through testing via physics the quality of the harmonics. We hope to write a program that identifies and models the differences in harmonics between old and new guitar strings. We will need to buy the two types of guitar strings and find old ones made out of the same material. After we have tested their harmonics we will measure the diameter of the strings and use physics formulas to discover the movement of the different strings. We also need to track down the equipment that will enable us to identify the frequencies that our strings produce. Our group is hoping to get a mentor to help us with the programming aspect of our project.

### Mathematical Equations for Properties of Vibrating Strings

Our approach to this project has been to learn HTML, C++, research Physics books and related projects on the Internet to gather the key physics equations. We are developing our code corresponding with these equations. Equations to find wavelength look like:

Wavelength = 2 * Length

Now that wavelength is known, it can be combined with the given value of the speed to calculate the frequency of the first harmonic for this given string. This calculation is shown below.

speed = frequency * wavelength

frequency = speed/wavelength

By finding the frequency of the guitar string one can find the musical capabilities of the string. In theory, an old string will have a varied frequency than a new string. Our project will not only prove that string frequency corresponds with age but also that frequency range varies for an older guitar string compared to newer. Eventually, we will test strings by the month to graph the gradual variation in frequency.

### Key Equations!

• V= speed = (distance)/(time) = d/t
• V = (frequency)(wavelength) = f*l
• f = # of waves/sec passing a point
• cps = cycles per second = Hertz = Hz
• Vsos=331.5m/s@ 0o Celsius + (.59m/s)(To Celsius)

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