IN CYLINDRICAL TUBES. 267 



experimenters, appeared either to contradict theory, or at least to be 

 altogether anomalous. According to our common notion on the subject, 

 an open tube gives the strongest resonance when its length is nearly 



equal to an even multiple of 7, instead of an odd multiple, as above 



stated ; and Savart* has given this as the result of his own experiments 

 for tubes of about the same diameter as those I have usually employedf ; 

 but asserting also that the length is less as the diameter is increased, 

 and this too whether the disturbance extend over the whole orifice of 

 the tube or not. My results, however, are entirely at variance with 

 this latter assertion, for I confidently conclude from them that if the 

 disturbance extend uniformly and equably over the orifice of the tube, 

 the phenomena will be independent of its diameter:]:, with the exception 

 of the effect it may have on the displacement of the nodes |. If, however, 

 the disturbance extend but partially over the orifice, I see no reason 

 to doubt the accuracy of the last-mentioned results of M. Savart ; and 

 this supposition will also account for the apparent discrepancy between 

 his results and mine as respects the length of the open tube (of which 

 the diameter does not much exceed an inch) producing the greatest 

 resonance; for it is manifest that with this partial disturbance none 

 of that condensation and rarefaction on the surface of the plate can 

 take place, which in my experiments necessarily attends, and may be 

 considered as causing, that powerful resonance of which I have spoken. 

 It is easily seen, in fact, that when the length of the tube is neany 



equal to an odd multiple of -, the phase of the waves reflected from 



any considerable part of the orifice not occupied by the vibrating plate, 

 will be directly opposite to that of the waves propagated by the plate 

 itself; and that thus a great part of the vibration within the tube will 

 be destroyed by interference. 



There is no difficulty, therefore, in explaining the non-existence of 

 resonance in this case. If the tube, however, be lengthened or shortened 



by about - , (still supposing the disturbance at its mouth partial), a 



* Annates de Chimie, Tom. XXIV. p. 56. t See Art. S6. 



t See Art. 36, p. 264. § Art. 36. 



