Lord Rayleigh on Bells. 3 



point of application of the blow be conceived to travel round 

 a circle symmetrical with respect to the axis, say, for brevity, 

 a circle of latitude, the displacement will make no difference 

 to the vibration considered as a whole, but the effect upon an 

 observer who retains a fixed position will vary. If the bell 

 be situated in an open space, or if the ear of the observer be 

 so close that reflexions are relatively unimportant, the sound 

 disappears as nodes pass by him, swelling to a maximum 

 when the part nearest to the ear is one of the places of 

 maximum normal motion, which for brevity we will call 

 loops. In listening to a particular note it would thus be 

 possible to determine the number of nodal meridians by 

 watching the variations of intensity which occur as the place 

 of the blow travels round a circle of latitude. 



In practice the symmetry is seldom so complete that this 

 account of the matter is sufficient. Theoretically the slightest 

 departure from symmetry will in general render determinate 

 the positions of the nodal systems. For each number of 

 cycles n, there is one determinate mode of vibration with 2n 

 nodes and 2n intermediate loops, and a second determinate 

 mode in which the nodes and loops of the first mode exchange 

 functions. Moreover the frequencies of the vibrations in the 

 two modes are slightly different. 



In accordance with the general theory, the vibrations of the 

 two modes as dependent upon the situation and magnitude of 

 the initiating blow are to be considered separately. The 

 vibrations of the first mode will be excited, unless the blow 

 occur at a node of this system ; and in various degrees, 

 reaching a maximum when the blow is delivered at a loop. 

 The intensity, as appreciated by an observer, depends also 

 upon the position of his ear, and will be greatest when a 

 loop is immediately opposite. As regards the vibrations of 

 the second mode, they reach a maximum when those of the 

 first mode disappear, and conversely. 



Thus in the case of n cycles, there are 2n places where the 

 first vibration is not excited and 2n places, midway between the 

 former, where the second vibration is not excited. At all 4n 

 places the resulting sound is free from beats. In all other 

 cases both kinds of vibration are excited, and the sound will 

 be affected by beats. But the prominence of the beats 

 depends upon more than one circumstance. The intensities 

 of the two vibrations will be equal when the place of the blow 

 is midway between those which give no beats. But it does 

 not follow that the audible beats are then most distinct. The 

 condition to be satisfied is that the intensities shall be equal 

 as they reach the ear, and this will depend upon the situation 



B2 



