Three successive resonance frequencies in an organ pipe are 1310, 1834 and 2358 Hz, respectively. What is the fundamental frequency?
Right, I know this is open at one end because the ratios of the frequencies come as 15:7 etc. I also know that where f_1 is the fundamental frequency.
What I did:
EDT: Let me know if this makes sense
I figured this would make more sense because n has to be odd? I plugged in 1310 for f_n and 1834 for f_n+1, rearranged for n and got n = 5 and hence f_1 = 262 Hz. Does that make sense?
I also confirmed this using the fact that for one open end, the frequencies come in ratios of 15:7... and given that 1310/1834 has a ratio of 5/7, eventually you find that 1310 is indeed 5 times f_1.
Hope that makes sense
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Last edited by trm90; 11-02-2010 at 19:53.
- 11-02-2010 19:16
- 11-02-2010 20:54
It makes sense ok.
the 3 frequencies are 5fo, 7fo and 9fo. and give the expected overtones in the odd harmonic series typical of a pipe closed at one end.