CAMS390 · Music · Uncategorized

First Tube Frequencies: 2.4m

Since I’m using LPG/Propane gas, the speed of sound in it is 258 m/s. (v)
The length of my pipe is 2.4m. (L)

Therefore, to calculate the wavelength, it will be:
λ = 4L
λ = 4*2.4
λ = 9.6

Therefore, the frequency will be:
f = v/λ
f = 258/9.6

f = 26.875


Now 26.875 is not a note on the standard tuning scale, but it is pretty close to A0 (given that A4 = 440hz, A3 = 220hz […] A0 = 27.5hz), so knowing this, it would be easier to calculate the correct length of pipe for A0 to be the fundamental frequency.

λ = v/f
λ = 258/27.5
λ = 9.3818181…

L = (1/4)λ
L = (1/4)9.381818181…
L = 2.345454545…

As this is smaller than 2.4m it is an achievable length to get.  Given that our tests were conducted with a piece of wood in the end about 5cm thick, it is likely that this is close to the frequencies we were playing around with (especially given that it responded well to the resonant frequencies of B4, C, and C#5 (18, 19, and 20).


To calculate the resonant frequencies, I’m using the formula f(n) = n*f(1).
Below is a list of the resonant frequencies in order.

  1. 27.5 – A0 (Fundamental Frequency)
  2. 55 – A1
  3. 82.5 – E2 (Standard tuning = 82.4069)
  4. 110 – A2
  5. 137.5 – C#3 (Standard tuning = 138.591)
  6. 165 – E3 (Standard tuning = 164.814)
  7. 192.5 – G3 (Standard tuning = 195.998)
  8. 220 – A3
  9. 247.5 – B3 (Standard tuning = 246.942)
  10. 275 – C#4 (Standard tuning = 277.183)
  11. 302.5 – D#4 (Standard tuning = 311.127)
  12. 330 – E4 (Standard tuning = 329.628)
  13. 357.5 – F4 (Standard tuning = 349.228)
  14. 385 – G4 (Standard tuning = 391.995)
  15. 412.5 – G#4 (Standard tuning = 415.305)
  16. 440 – A4
  17. 467.5 – A#4 (Standard tuning = 466.164)
  18. 495 – B4 (Standard tuning = 493.883)
  19. 522.5 – C5 (Standard tuning = 523.251)
  20. 550 – C#5 (Standard tuning = 554.365)
  21. 577.5 – D5 (Standard tuning = 587.330)
  22. 605 – D#5 (Standard tuning = 622.254)
  23. 632.5 – D#5 (Standard tuning = 622.254)
  24. 660 – E5 (Standard tuning = 659.255)
  25. 687.5 – F5 (Standard tuning = 698.456)
  26. 715 – F5 (Standard tuning = 698.456)
  27. 742.5 – F#5 (Standard tuning = 739.989)
  28. 770 – G5 (Standard tuning = 783.991)
  29. 797.5 – G5 (Standard tuning = 783.991)
  30. 825 – G#5 (Standard tuning = 830.609)

As it’s results are based on frequencies, rather than standard tuning scales, the only notes that are pure will bee the A notes.  This is something that will need to be considered in the future.  Do I stick to the standard scale or delve into microtonal areas?

 

 

 

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