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= Strumming Some Science =

Specific Question How does tension affect the frequency of a note of a string on a guitar?

Broad Question
Does tension affect the frquency/note of a guitar string?

Hypothesis
It is hypothesized that a higher tension would produce a higher note on the guitar.

Graph of Hypothesis
(Sheet 4) media type="custom" key="15618832"

Variables
**Independent Variable:** Tension **Dependent Variable:** Frequency (Hertz) **Controlled Variables:** Method of tightening strings, way to measure tension, string's thickness

Vocabulary List That Needs Explanation
•**Newtons** - The SI unit of force. It is equal to the force that would give a mass of one kilogram an acceleration of one meter per second per second, and is equivalent to 100,000 dynes. •**Hertz** - The SI unit of frequency, equal to one cycle per second •**Frequency** - The rate at which something occurs or is repeated over a particular period of time or in a given sample

General Plan
In this experiment it will be determined how string tension effects the frequency of a string on a guitar. To do this, one end of a low E string will be attached to a guitar tuning peg. The other end of the string will be clamped to a High Resolution Force Sensor. Start out at 20 newtons of tension. Pluck the string and record the note. Go up to 25 newtons of tension, pluck the string and record the note. Keep increasing the tension by 5 newtons until the string snaps or tension reaches 40 newtons and record the pitch each time. Repeat this process for the other 5 strings. Record the pitch and the tension in a data table. Be cautious and wear eye goggles in case the string snaps from too much tension.

Safety Or Environmental Concerns
Strings could snap/break - wear goggles for protection

Resources and Budget Table

 * Tuner/Audacity - Have it
 * H.R.F.S - get from Mr. Yahna
 * Set of Guitar Strings - Have it
 * A counter to clamp the string on - In science room
 * Clamp - get from Mr. Yahna
 * Guitar tuning peg set - Have it
 * Hertz frequency chart - Get online

Data Table
Tuning ||  -20 N ||  -25 N || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;"> -30 N || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;"> -35 N || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;"> -40 N ||
 * ||  || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Note: ||   ||   ||   ||   ||
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Tension || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Standard
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">String 1 || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Low E || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">A <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;"># || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">B || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">C || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">C <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;"># || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">D ||
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">String 2 || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Low A || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">C || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">D <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;"># || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">F || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">G <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;">b || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">A <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;"># ||
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">String 3 || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Low D || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">A || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">G <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;"># || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">A || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">F <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;"># || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">B ||
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">String 4 || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Low G || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">A || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">C || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">D || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">? || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">? ||
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">String 5 || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">High B || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">E <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;">b || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">G <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;"># || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">A || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">A# || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">A ||
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">String 6 || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">High E || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">D || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">D <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;"># || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">E || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">F || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">F <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 9px; text-decoration: none; vertical-align: super;"># ||

Time Line
Complete design and collection of all materials: before 3/5/12 <span style="background-color: transparent; display: block; font-family: 'Times New Roman'; font-size: medium;"><span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">Test setup of project, do not collect data: 3/7/12 - 3/9/12  <span style="background-color: transparent; display: block; font-family: 'Times New Roman'; font-size: medium;"><span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;"> Official trial with collection of data: 3/15/12 - 3/21/12  <span style="background-color: transparent; display: block; font-family: 'Times New Roman'; font-size: medium;"><span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">Finish all data analysis: before 3/26/12  <span style="background-color: transparent; display: block; font-family: 'Times New Roman'; font-size: medium;"><span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;"> Complete results and conclusion: before 3/31/12

Background Research
> References [|http://www.google.com/search?hl=en&q=newton's&tbs=dfn:1&tbo=u&sa=X&ei=peCGT87PK6XB0AHG4_SzBQ&ved=0CCoQk] [|Q4&biw=1024&bih=677] [|http://www.google.com/search?hl=en&biw=1024&bih=677&tbs=dfn%3A1&q=hertz&oq=hertz&aq=f&aqi=g10&aql=&gs_l=serp.] [|3..0l10.25720l54673l0l54874l5l5l0l1l1l0l135l408l3j1l4l0.frgbld.] [|http://www.google.com/search?hl=en&biw=1024&bih=677&tbs=dfn%3A1&q=frequency&oq=frequency&aq=f&aqi=g10&aql=&g] [|s_l=serp.3..0l10.12842l14722l0l14957l9l9l0l1l1l0l140l552l2j3l5l0.frgbld.] <span style="display: block; font-family: Georgia,'Times New Roman',Times,serif; font-size: 1.1em; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px; text-align: left;">**Detailed Procedure** <span style="background-color: transparent; display: block; font-family: 'Times New Roman'; font-size: medium;"><span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">1. Place one end of a guitar string onto a tuning peg and tie the other end to a H.R.F.S. (High Resolution Force Sensor) 2. Tighten that string to 20 newtons of tension. 3. Pluck string and use tuner to record the note. <span style="background-color: transparent; display: block; font-family: 'Times New Roman'; font-size: medium;"><span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">4. Use Hertz frequency chart to see what frequency the note is equivalent to. <span style="background-color: transparent; display: block; font-family: 'Times New Roman'; font-size: medium;"><span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">5. Write down the frequency. 6. Increase the tension by 5 newtons and repeat steps 3-5 for all other strings. (stop if string snaps or if you reach 40 newtons)
 * Newtons
 * Hertz
 * Frequency

Photo List

 * <span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">Picture of string clamped to table
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">Picture of snapped string
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">Picture of Tuner picking up the note
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">Whole setup with plucked string
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">H.R.F.S.
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;">Picture of Computer

Results
**All Raw Data** <span style="background-color: transparent; display: block; font-family: 'Times New Roman'; font-size: medium;"> <span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;"> When the experiment was conducted results had a pattern. With the high E string, the frequency would increase by an average of 20 Hz when the tension increased by intervals of 5 newtons. With the G string, when tension increased by 5 newtons, the frequency would increase by an average of 10 Hz. Overall, when the tension of a string was increased, the frequency would increase with it. Graph (Sheet 1) media type="custom" key="14167234" Graph media type="custom" key="14168610" Photos

Conclusion
<span style="background-color: transparent; display: block; font-family: 'Times New Roman'; font-size: medium;"> <span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 15px; text-align: left; text-decoration: none; vertical-align: baseline;"> This experiment was conducted to see how tension could effect the frequency of a note produced by a guitar. The dependent variable was tension, the independent variable was frequency in Hertz. After conducting the experiment, it was concluded that when tension is increased, the frequency would increase with it. For the high E string, the frequency would increase by an average of 20 Hz when the tension increased by 5 newtons. With the G string, when tension increased by 5 newtons, the frequency would increase by around 10 Hz. This data supports our conclusion.

Discussion
<span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 16px; text-align: left; text-decoration: none; vertical-align: baseline;">The question was how does tension effect the frequency of a note on a guitar. It was hypothesized that when the tension increased, the frequency would increase. After the experiment was conducted, the question was answered. When the tension increased, the frequency would increase. Results of the high E and G string supported this answer. The high E string had a pattern of increasing about 20 Hertz every five newtons. The hypothesis was supported by the results. It was surprising that the strings wouldn't snap. It was expected that the string would snap after the tension was higher than forty newtons. Most of the string's frequencies increased as the tension increased. The only problem that occurred was that the tuning knob would not turn any farther so the last two notes for the last two tension intervals were not able to be recorded. The experiment did not change when it was in process. One thing that could be improved is the method of tightening the strings. To conduct this experiment a High Resolution Force Sensor was needed to measure force (newtons) and a tuner to measure the note. We clamped the H.R.F.S and the tuning peg to the table with a clamp. This cannot improve technology in the future for someone doing this experiment. This experiment is not needed for the future and people in the future will probably not gain from this. This is not a big breakthrough in information or technology.

Benefit to Community and/or Science
It doesn't appear that the community or science can benefit with this experiment.

Abstract

 * This experiment was conducted to see how tension could effect the frequency of a note produced by a guitar. The dependent variable with the tension, the independent variable was the frequency in Hertz (Hz). After conducting the experiment, it was concluded that when tension is increased, the frequency would increase with it. For example, the high E string’s frequency would increase by an average of 20 Hz when the tension increased by 5 newtons. With the G string, when tension increased by 5 newtons, the frequency would increase by around 10 Hz. It was hypothesized that these results would happen. **