Building PVC Instrument by the Formulas
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Transcript of Building PVC Instrument by the Formulas
Building an Instrument from Formulas
Lenore Horner
The Seven Hills Schools
April 18, 2015
Goal
Starting Point
End Correction
Finger Holes
Outline
1 Goal
2 Starting Point
3 End Correction
4 Finger Holes
Lenore Horner (7 Hills) Instrument April 18, 2015 2 / 8
Goal
Starting Point
End Correction
Finger Holes
Goal
Have my physics students build PVC flutes based on simpleextensions of the formulas for standing waves.
The pipes are cylindrical and open at both ends. (Quick check:overblow a transverse flute and the frequency doubles)
Lenore Horner (7 Hills) Instrument April 18, 2015 3 / 8
Goal
Starting Point
End Correction
Finger Holes
Basic Formulas
string; open pipe
f =nv
2L(1)
n = all integers (2)
stopped pipe
f =nv
4L(3)
n = odd integers (4)For this project, only worry about the fundamentals so n = 1 fromnow on.
Lenore Horner (7 Hills) Instrument April 18, 2015 4 / 8
Goal
Starting Point
End Correction
Finger Holes
End Correction Approximation
It takes time for the information that the pipe has ended topropagate to the center of the column of air in the pipe.
stopped pipe: standard correction
f =v
4(Lcorr + 0.3D)(5)
D is the interior diameter of a cylinder
This can be approximately motivated by the idea that we have toadd a cylinder with volume equal to the hemisphere at the end ofthe pipe.
1
2
4
3πr3 = πr2Lextra (6)
Lextra =2r
3=
D
3(7)
Lenore Horner (7 Hills) Instrument April 18, 2015 5 / 8
Goal
Starting Point
End Correction
Finger Holes
Testing End Correction
pipe dimensionslength: 28.0 cminterior diameter: 2.0 cm
results
f =v
4L= 306 Hz (8)
f =v
4(L+ 0.3D)= 300 Hz (9)
fplayed = 298 Hz (10)
Lenore Horner (7 Hills) Instrument April 18, 2015 6 / 8
Goal
Starting Point
End Correction
Finger Holes
Hall
Formulas for ONE Hole
te = wall thickness pipe + 0.8Dh − 0.5D2
h
Dp(11)
y = Lcorr, lowest − Lcorr, current (12)
x =te
r2 + tey
(13)
Ldrill hole at = Lcorr, current − x (14)
Lenore Horner (7 Hills) Instrument April 18, 2015 7 / 8
Goal
Starting Point
End Correction
Finger Holes
Reality Check: 1”
starting from empirical end correction for each end of the flute
Lenore Horner (7 Hills) Instrument April 18, 2015 8 / 8
Goal
Starting Point
End Correction
Finger Holes
Reality Check: 1-1/4”
starting from empirical end correction for each end of the flute
Lenore Horner (7 Hills) Instrument April 18, 2015 9 / 8