IN CYLINDRICAL TUBES. 257 



tube*. It is only however as regards the intensity of the vibrations 

 that this precaution respecting the relative position of the nodal 

 lines and mouth of the tube is important ; it does not affect the 

 positions of the nodes. The reason is obvious — it does not affect the 

 value of X. 



30. Again, taking the tube open at B, let the extreme section 

 at A be made to coincide nearly with the surface of the vibrating 

 plate. If the plate (the bow being applied to it) vibrate freely, let 

 the length of the tube be gradually increased or diminished. It will 

 thus be found, that as the tube approximates to certain lengths, the 

 plate vibrates with less facility, requiring a greater pressure of the 

 bow, and continuing to vibrate audibly for a shorter time after its 

 removal; and in many cases, between certain limits in the length of 

 the tube, it becomes almost impossible to make the plate assume that 

 state of vibration which it assumes freely for other lengths ; and the 

 vibration, if it be produced, appears to cease almost instantaneously 

 on the removal of the bow, instead of being audible for several 

 seconds, as it would be if the tube were removed, or were of a 



different length. These phenomena recur for every increase of — in 



the length of the tube ; and if I be any length with which it becomes 

 almost impossible to make the plate vibrate in the manner proposed, 



then will / + - be that length with which it vibrates with the same 



facility as if the tube were removed. 



* It is easy by a very simple experiment to give ocular demonstration of the fact that the 

 union of two intense sounds may produce perfect silence. Take a branch tube ABA' (Fig. 3.),"and 

 stretch over the open end B a fine membrane or a piece of common writing paper. Place the 

 open extremities A, A' of the equal and similar branches CA, CA' over portions of two ventral 

 segments of a vibratory plate in the same phase of vibration. A small quantity of sand strewed 

 over the membrane at B, will immediately shew it to be in a state of strong vibration. Let A, A 

 be then carefully placed over suiiilar portions of similar ventral segments of the plate, in opposite 

 phases of vibration ; the sand on the membrane will remain perfectly at rest, shewing that the 

 waves propagated along AC and A'C in opposite phases so completely interfere at Cas to produce 

 no undulation along CB. In other words, no sound would in this case be transmitted along the 

 tube to its mouth B. 



