Question

Problem 3: A certain pipe has resonant frequencies of 234 Hz, 390 Hz, and 546 Hz, with no other resonant frequencies between these values. (Hint: The lower frequency is not necessarily the pipe fundamental frequency) (a) Show that the difference of frequency between two adjacent harmonics has the same expression for a pipe open at both ends as for a pipe closed at one end (b) How long is this pipe? (c) Is this a pipe open at both ends or closed at one end? (d) What is the fundamental frequency of this pipe?

Answer 1

w frequency of pipe closed at one end is given by f = (2nte) u Next frequency of bibe as fg ? (216+1) 7s) fg = (2n+370 fy_f= (2013-20+) ~ fe f = 9 27 of pipe frequency open at both end ť z nr - 2L fez (mt) v -.f-fyz n+1-n) e f-fx =

so difference between adjacent has monics is same for both pibes. O speed of sound = 343 mis 2L 320Hz-234 H2 34zm1s N56 zu ~ 23 1017 If resorant frequency ies integral multiple of I then, pube will be open): ml) = 234H2 - mx 256H2 = 234H2 m = 105 not a categeo. Pibe is closed of one end • fundamental frequency of closed organ pipe. to = v L = 2 2 2 2 2 to = 1/2 X 156H2 to = 7842