27tt Mb HOPKINS ON AERIAL VIBRATIONS IN CYLINDRICAL TUBES. 



according to theory, if the cause maintaining the vibratory motion in 

 a tube be suddenly changed, (as in passing from one note to another), 

 the effect of the former mode of disturbance on the form of the 

 succeeding vibration will become inappreciable in an exceedingly short 

 period of time. Now in the most rapid musical passages, the number 

 of notes played in a second never probably exceeds ten or twelve, 

 and these usually embrace only the higher notes of the scale, for 

 which there must be many hundred vibrations in a second. Suppose 

 this number, however, not greater than about two hundred ; any undula- 

 tion transmitted from the reed or embouchure would still be reflected 

 about twenty times at the open end in the interval between two 

 consecutive notes in the most rapid musical passage. Now assuming 

 unity to represent the intensity of a wave incident at the open extremity 

 of the instrument*, let 1 — )3 represent that of the reflected wave, 

 (1 — /3)". will represent (at least sufficiently approximately) its intensity 

 after n reflections ; and consequently, as we have no reason to suppose /3 

 very small as compared with unity, it is probable that after five or six 

 reflections, the intensity of this wave will be quite inappreciable. Hence 

 the apparently instantaneous cessation of sound after the exciting cause 

 has ceased, and the most rapid transition from one note to another, 

 are perfectly accordant with theory. 



M. Poisson, in the Memoir referred to in the early part of this 

 paper, has also investigated the vibratory motion of air in two tubes 

 of different diameters united together at one extremity. I hope to 

 examine this case also experimentally. His results must necessarily be 

 erroneous, as far as they depend on the physical condition he has assumed 

 to exist at the extremity of the open tube, and which I have shewn to 

 be inconsistent with observed phenomena in the uniform tube. 



* See Art. 14. 



W. HOPKINS. 



St Peter's College, 

 i\r««/ 20, 1833. 



