Fifth overtone of an open pipe of length L₀ is in unison with the fifth overtone of the pipe closed at one end of length L_c . The ratio L₀ to L_c is

Step-by-step solution

For an open pipe, the frequency of the n -th harmonic is given by f = n v 2L₀ . The fundamental frequency corresponds to n=1 . The fifth overtone corresponds to the 6th harmonic, so n=6 . Frequency of the fifth overtone of the open pipe is f_o = 6 v 2L₀ = 3v L₀ . For a pipe closed at one end, the frequency of the m -th harmonic is given by f = m v 4L_c , where m takes only odd integer values ( m = 1, 3, 5, ). The fundamental frequency corresponds to m=1 . The first overtone is m=3 , the second is m=5 , and so on. T