3/26/2014 Master Ithttp://www.webassign.net/v4cgi/questions/tutorial_popup.tpl 1/2Master ItTwo adjacent natural frequencies of an organ pipe are determined to be 561 Hz and 663 Hz. (Assume thespeed of sound is 343 m/s.)(a) Calculate the fundamental frequency of this pipe.(b) Calculate the length of this pipe.Part 1 of 4 ConceptualizeThese harmonics are fairly high, higher than the A above middle C, which is 440 Hz. We expect the pipe to bea long one, corresponding to a low a bass note.Part 2 of 4 CategorizeWe use the model of a wave under boundary conditions. We are not told in advance whether the pipe is openat one end or open at both ends, so we must think about both possibilities.Part 3 of 4 AnalyzeFor both open and closed pipes, resonant frequencies are equally spaced as numbers. We are given twoadjacent frequencies of 663 and 561 Hz. The difference between these two values is 102Hz, the remaining frequencies down to and including the fundamental frequency are given by the following.(Enter your answers from largest to smallest.)(a) These are oddinteger multiples of the fundamental frequency of 51 Hz.Part 4 of 4 AnalyzeBecause the step size is twice the fundamental frequency, we know the pipe is closed, with an antinode at theopen end, and a node at the closed end. The wavelength is four times the pipe length, so we haveFinalize 459 Hz 357 Hz 255 Hz 153 Hz 51 HzdNA = = = = 1.68 m.λ4v4f343 m/s4 51 s−13/26/2014 Master Ithttp://www.webassign.net/v4cgi/questions/tutorial_popup.tpl
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