17 December 2017
- Last edited 17 December 2017
I am gradually learning the ACT Acoustics Extension and worked most of the workshops that came with the documentation.
I am reading “The Science of Sound” 2nd Edition by Thomas D. Rossing. Example 4.3 is to find the first three modes of vibration of a pipe 750 mm long with one open end and one closed end (neglect end correction). The answer in the book is f1 = v/4L = 343/4(0.75) = 114 Hz, f2 = 3(343)/4(0.75) = 343 Hz and f3 = 5(343)/4(0.75) = 572 Hz. These frequencies are calculated from knowing the standing wave patterns of the first three modes. I built a Modal Acoustics model in ANSYS 18.2 and got excellent agreement.
Rossing provides a formula to calculate the frequency of a Helmholtz resonator in Section 2.3 and gives an example of a flask with a 980 mm diameter sphere, a 30 mm diameter neck that is 100 mm long.
Rossing formula f = 207 Hz
Acoustic model f = 232 Hz.
CYLINDER by Emir
Your formula f = 262 Hz
Acoustic model f = 299 Hz
Rossing formula f = 346 Hz
Rossing says that open pipes have an “end effect” that adds to the length of typically 0.61D, while the formula you gave seems to have an “end effect” correction of 0.75D. I find it interesting that if I zero out the end correction in your formula, I get the same value as the Rossing formula.
If I use a correction of 0.35D, then I get f = 298 Hz, which is very close to the acoustic model.
I hope some of this is useful for you.