Singing corrugated pipes revisited

A long corrugated tube open at both ends sings notes which depend on the flow velocity of air flowing through the tube. The notes it sings are natural harmonics of the tube. In 1974, Crawford suggested an explanation for this: A given note will sing when the flow velocity is such that the ‘‘bump frequency’’ equals the frequency of the note, provided also that the flow velocity is sufficiently high to induce turbulent flow. He suggested two theories to explain the singing in terms of turbulence. One assumed that the onset of turbulence agrees with the classic Reynolds number for smooth tubes (Rsmooth≊2000) in which the characteristic length of the object that has air flowing in is equal to the diameter. The second assumed the characteristic length of the object was equal to the distance between the corrugations. Crawford reported having good agreement between the classic diameter-induced turbulence theory and experiment for some pipes. However, for other tubes he observed singing at Reynolds numbers that were much smaller than the classical result of 2000. For these, he could not establish if he was observing corrugation-induced turbulence. (He stated he did not have sufficient pipes.) After looking at a variety of tube diameters and corrugation lengths, we also observed (as Crawford reported) that some of the data agreed with the classic diameter-induced turbulence, and some did not. Ironically, the hypothesis Crawford introduced (and rejected) as an alternative possibility seems to fit ALL of our data quite well. A new Reynolds number associated with the onset of turbulence for corrugated pipes is presented: Rcorr≊500.