I made a pan flute with copper tubing (3/4 in diameter) to correspond to the following notes/lengths:
C - 15.4cm
D - 13.6cm
E - 12.0cm
G - 9.8cm
A - 8.7cm
The original instructions called for PVC pipe at 1/2in diameter, so the notes are off.
How do I change the measurements of the pipes with those notes to fit the copper volume and 3/4in diameter of the tubing?
Extra note: I'm planning to cut up some more copper to build other notes to play a C major scale, so if I know how to do this, I can probably cut more to make a bigger pan flute.
Thank you!
To modify the lengths of the copper tubing to match the desired notes and accommodate the 3/4 inch diameter tubing, you will need to perform some calculations using the principles of pipe acoustics. Here's how you can do it:
1. Determine the pitch of each note: The length of a pipe affects its pitch, and shorter pipes produce higher pitches. You already have the desired lengths for each note.
2. Convert the lengths to account for the 3/4 inch diameter tubing: The length of the tubing required for each note will be longer than the desired length due to the larger diameter. To find the correct lengths, you can use the relationship between pitch and pipe length.
3. Calculate the adjusted lengths: To calculate the adjusted lengths, you can use the formula:
Adjusted Length = Desired Length + (Diameter Change Adjustment)
To find the Diameter Change Adjustment, use the following formula:
Diameter Change Adjustment = (π * Diameter Change) / 4
Where:
- π is a mathematical constant approximately equal to 3.14159
- Diameter Change = (3/4 inch - 1/2 inch) = 1/4 inch
4. Substitute the values: Plug in the values for each note to calculate the adjusted lengths. Here are the calculations:
For C:
Adjusted Length = 15.4 cm + ((π * 1/4 inch) / 4)
For D:
Adjusted Length = 13.6 cm + ((π * 1/4 inch) / 4)
For E:
Adjusted Length = 12.0 cm + ((π * 1/4 inch) / 4)
For G:
Adjusted Length = 9.8 cm + ((π * 1/4 inch) / 4)
For A:
Adjusted Length = 8.7 cm + ((π * 1/4 inch) / 4)
5. Perform the calculations: Evaluate the formulas to compute the adjusted lengths for each note.
For example, for C:
Adjusted Length = 15.4 cm + ((3.14159 * 1/4 inch) / 4) = [perform the calculation]
Continue this process for each note to calculate their respective adjusted lengths.
By following these steps, you should be able to determine the adjusted lengths for each note to accommodate the 3/4 inch diameter tubing. Make sure to double-check your calculations and make precise cuts to achieve the desired pitches. Good luck with building your pan flute!
To change the measurements of the pipes to fit the copper volume and 3/4 inch diameter tubing, you need to consider the relationship between the diameter of the tubing and the length of the pipe required to produce a specific pitch.
The pitch of a pipe is determined by its length, and in the case of a closed tube (like your pan flute), the fundamental frequency of a pipe is inversely proportional to its length. This means that as the length of the pipe decreases, the pitch increases.
You already have the lengths of the original notes using PVC pipe at 1/2 inch diameter, so now you need to calculate the corresponding lengths for the new copper tubing with a 3/4 inch diameter.
To find the new lengths, you can use a formula that relates the length and diameter of a pipe to its pitch. This formula is given as:
L1 / L2 = (d2 / d1) * √(f1 / f2)
where L1 and L2 are the lengths of the original and new pipes, respectively, d1 and d2 are the diameters of the original and new pipes, and f1 and f2 are the frequencies (or pitches) of the original and new notes, respectively.
In this case, you know the lengths and frequencies of the original notes and the diameter and desired pitch of the new notes. Rearranging the formula, you can solve for L2, the length of the new pipes:
L2 = (L1 * d2 * √(f2 / f1)) / d1
Using this formula, let's calculate the new lengths for each note:
For note C:
L1 = 15.4 cm
d1 = 1/2 inch = 1.27 cm
d2 = 3/4 inch = 1.91 cm
f1 = frequency of C
You need to select the desired frequency of C for your pan flute. Let's assume it is 261.63 Hz, which is the standard frequency for middle C. Now, we can calculate L2:
L2 = (15.4 * 1.91 * √(f2 / 261.63)) / 1.27
Using this formula, you can calculate the new lengths for each note by substituting the values for L1, d1, d2, f1, and f2, where f2 is the frequency you choose for each note.
Remember to cut the copper tubes to the calculated lengths and adjust them as needed to fine-tune the pitches.