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    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 1:3:5:7 etc. I also know that f_n = nf_1 where f_1 is the fundamental frequency.

    What I did:

    EDT: Let me know if this makes sense

    f_n = nf_1



    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 1:3:5:7... 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

    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.
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Updated: February 11, 2010

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