Pluck+that+strayng

Group Members: Tina B. and Max S. Goal: Find out how tension affects the pitch a string vibrates at.

__**Procedure**__ 1. Assemble a physics stand using two metal rods and two clamps. Using one clamp, attach the metal rods perpendicularly so that they create a "T" shape. Use the other clamp to fasten the T-shaped stand to the edge of a classroom table. 2. Find a spool of thread. Cut a length of string equivalent to 80.5 centimeters. Tie one end of the string to the horizontally-positioned metal rod. 3. Tie the bottom 6 centimeters of the string into a loop. 4. Collect four different hanging masses (make sure there is considerable difference in weight, and do not exceed 2.5 Newtons, as the string is not capable of handling more). Log their masses in kilograms and newtons (you will have to convert) in a data table. 5. Open a pitch-measuring web-page, such as [] 6. Hook each hanging mass onto the loop at the bottom of the string. 7. Pluck the string, and find the pitch it produces using the pitch-measuring webpage. Record this in the data table. 8. You will notice on the pitch-measuring webpage that the frequency in Hertz of each pitch is listed. Log this frequency value in your data table. 9. Repeat steps 6, 7, and 8 for the three remaining hanging masses.


 * __Evidence__**


 * Data:**
 * = Mass (kg) ||= Newtonic Weight (N) ||= Pitch Produced ||= Frequency (Hertz) ||
 * = 1.0 ||= 9.8 ||= Low A ||= 110 ||
 * = 1.5 ||= 14.7 ||= Low C ||= 130.81 ||
 * = 2.0 ||= 19.6 ||= Low D# ||= 155.56 ||
 * = 2.5 ||= 24.5 ||= D# ||= 311.15 ||


 * Graph:**

F(x)=-427+114.5x-7.846x^2+.1798x^3
 * Equation relating frequency and weight:**

F(x)=Frequency in Hz x=Weight in N

We found that increasing tension on a string results in the string vibrating at a higher pitch (and frequency). While conducting our experiment, we found an equation that describes the relationship between tension and pitch of the string we used: F(x)=-427+114.5x-7.846x^2+.1798x^3. where F(x)=frequency of the string, and x=newtons of force on the string. This equation was created from data collected during four trials. In the trials, we varied the amount of mass on the string. We started with the lightest mass, 1 Kg, resulting in a pitch of a low A (110 Hz). Then we raised the amount of mass at the end of the string in increments of .5 Kg. 1.5 Kg resulted in a Low C (130.81 Hz), 2 Kg resulted in a Low D# (155.56 Hz) and 2.5 Kg resulted in a D# (311.15 Hz). The pitch is the frequency at which a string vibrates. As is evident from our experiment, by increasing the tension on the string, the string vibrates faster, causing a higher frequency. This makes sense because the more stress you put on a string, the faster it will vibrate at. When we plug in the weight in newtons into our equation, we basically got our answers back. It is not exact because of rounding errors in the step when deciding the pitch. The pitch produced is affected by tension, length, and gauge of the sting. If we used different length string or different gauge string, our results would be different. If the tension increases, then the pitch increases. If the tension decreases, then the pitch decreases. Because of these relationships, tension is affects pitch directly.
 * Conclusion:**