Upload
lee-golden
View
221
Download
1
Embed Size (px)
Citation preview
Where We Left Off…
Pipes Completed
Frame Needed to be Built
Objective- Portability, Easy to Assemble
Legs and Lower Frame
More PVC
The Finished Project
Not screwed together, straps needed for support
Playable in the same way as a xylophone
New “mallet”- Wood with mouse pad that is looser
Off?
Note Desired FrequencyTube Length Estimate Freq Ratios Length Exact
Difference- Estimate to Exact
Ratios to Exact
C 130.81 48.27814196 49 48.25 0.028141962 0.721858038
C#/Db 138.59 45.61006386 46.2315 46.25 -0.639936143 0.621436143
D 146.83 43.0925475 43.659 43.23 -0.137452496 0.566452496
D#/Eb 155.56 40.71629114 41.1845 41 -0.283708858 0.468208858
E 164.81 38.47317365 38.8815 37.75 0.723173655 0.408326345
F 174.61 36.35595756 36.71 36 0.355957563 0.354042437
F#/Gb 185 34.35625 34.643 33.75 0.60625 0.28675
G 196 32.47018495 32.7075 32 0.470184949 0.237315051
G#/Ab 207.55 30.70498073 30.8455 31.5 -0.795019272 0.140519272
A 220 29.00980114 29.1305 28 1.009801136 0.120698864
A#/Bb 233.08 27.42391561 27.489 26.25 1.173915608 0.065084392
B 246.94 25.9267889 25.945 25.25 0.676788896 0.018211104
C 261.63 24.51316267 24.5 25 -0.486837328 -0.013162672
Some lengths were off.
First, the estimate from the equation (Length=12434.3125/(2*Frequency) + Radius)
Second, estimate based on frequency ratios
Third, exact measurement from instrument
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10 11 12 13
Series1
Tubes
0
10
20
30
40
50
60
130.81146.83164.81185
207.55233.08261.63
Frequncy
Length
Tube Length EstimateFreq Ratios Length
Exact
Is the Pitch Off?Predicted Pitch Pitch Desired Freq. Actual Freq. Difference
Predicted length
Actual Length Difference
48 48.25 130.81 132.715498 1.905498 47.59574391 48.25 0.654256
49 49.1 138.59 139.394167 0.804167 45.35126555 46.25 0.898734
50 50.1 146.83 147.682975 0.852975 42.84798887 43.23 0.382011
51 51 155.56 155.563492 0.003492 40.71539404 41 0.284606
52 52.05 164.81 165.290467 0.480467 38.3635197 37.75 -0.61352
53 53.05 174.61 175.11915 0.50915 36.25243506 36 -0.25244
54 54 185 184.997211 -0.00279 34.35675658 33.75 -0.60676
55 55 196 195.997718 -0.00228 32.47055427 32 -0.47055
56 56 207.55 207.652349 0.102349 30.69021636 31.5 0.809784
57 57.3 220 223.845532 3.845532 28.52431467 28 -0.52431
58 58.1 233.08 234.43211 1.35211 27.27007116 26.25 -1.02007
59 58.8 246.94 244.105284 -2.83472 26.21915885 25.25 -0.96916
60 59.85 261.63 259.368544 -2.26146 24.72035563 25 0.279644
Using a chromatic tuner, found each pitch difference in cents
Used the equation 440*2^((Pitch-69)/12) to get the actual frequency
Frequency Difference
-4
-3
-2
-1
0
1
2
3
4
5
1 2 3 4 5 6 7 8 9 10 11 12 13
Series1
Sound
Pipe, 2 open ends
Wave Equation
∂²p/∂²x² = 1/c²*∂²p/∂t²
End Correction-
From Benson
Effective length longer than actual length by approx. 3/5 of tube width
-Sound coming out of it
If this were the case, each would have to be shorter
Difference is scattered, both + and -
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10 11 12 13
Series1
Could then be cutting error