Music Experiment

Procedure

We made an apparatus such that a wire could be stretched over the two screws and a weight attached to one end of the wire such that there was a particular tension in the string so that a note could be played. We had two different sized wires (the diameters varied), we kept the length of the wire constant, and varied the tension. We plucked the wire and compared the pitch produced with that of Allison's flute.

Results

For our results, we compared the pitch of the wire with that of Allison's flute. Many times the note we got from the wire was not an actual note that could be played. This is called a "quarter tone" because it is inbetween two half-notes (a half note is a half step in between a second interval. The half notes are usually the sharps and flats). When we got quarter tones we noted this or added more weight until we got a note we could play on the flute.

The equation that should be satisfied is:

frequency = (1/2L)*sqrt(tension/mass) where L is the length of the wire, and mass is the mass of the wire of length 1 meter. Also the tension = weight*9.8

The Length of the wire was .3683 meters.

Mass of the large wire was .001439 Kg/meter.

Mass of the small wiire was 3.753x10^-4 Kg/meter.


Small Wire

Weight (g)Force (N)Pitch ProducedExperimental Frequency (Hz)Calculated Frequency (Hz)
150 1.47C-sharp97.1184.96
2502.45E-flat108.15109.69
3503.43A-flat103.83129.79
4504.41B-flat116.54147.16
5505.39C183.33162.69
6506.37C-sharp193.49176.87
7507.35D205.78189.99
8508.33E-flat216.31202.26
9509.31E229.1213.82

Large Wire

Weight (g)Force (N) Pitch ProducedExperimental Frequency (Hz)Calculated Frequency (Hz)
450 4.41 A-flat 51.9175.15
550 5.39 A 11083.09
650 6.37 quarter tone between B and C
7507.35 C 91.6797.02
850 8.33 C-sharp97.12103.29
950 9.31 Indistinguished pitch

The frequencies we should have gotten are based on the ratios of the note found compared to the note C. An A has a frequency of 440 Hz, so we then solved for the other frequencies based on this and the ratios between pitches. Another ratio we used was that of a half step which is 1.05946. This gave us the frequency of the note in a certain octave. Since our notes were not in this octave, we used the ratio of 1:2 for octaves in order to get the frequency of the note in the actual octave.