2) DIY Flute making and speed of sound
The speed of sound through air depends on temperature, humidity, pressure,
carbon dioxide content, and other minor factors. But the biggest factor is
the temperature. As a rough estimate,
Vs = 20 * sqrt(T+273)
Where
Vs = speed of sound in m/s
T = temperature of air in degree Celsius
At 25 deg. C, Vs is about 345 m/s
Consequently, we can find the wavelength of sound in air as Vs / F
Where F = frequency of tone in cycles per second (Hz)
Now we get the frequencies of the various tones. There are many different tonality
formulae but we shall use the piano's tuning here. First, the frequency of A is 440 Hz.
The frequency ratio of each halftone is 2 to the power 1/12, which is about 1.06. The
frequency of other tones is calculated accordingly. Details can be found in the
following musical temperament page.
We can make a flute knowing that the length of a flute (measure from the mouth to
centre of the first open hole, with compensations for both ends) to make a tone is
half of its wavelength. That is Vs / F / 2. Due to end effects near the mouth and
end of tube, the actual length needed is somewhat shorter. As a rough rule, subtract
3 times the diameter of the tube. The actual calculation is much more complicated
and so the figures given below is just an approximation.
f/Hz 
L/mm 
296.7 
548 
329.6 
484 
349.2 
427 
392.0 
400 
440.0 
352 
493.9 
310 
523.2 
271 
If we just want to make a working flute, we finish here. However, if we want to
make a really accurate flute, we need to use a tuner to check the frequency of
each note. First we bore smaller holes. Then we check the tones with our tuner.
If it is flat, we bore the hole closer to the month and vice versa. Finally,
use a big drill to expand all holes to same size. The final diameter of the flute
holes is about 10 to 12mm. We can begin with a 6mm hole and expand the holes in the
right direction under the guidance of a tuner.
