RESONANCE. 1177 



intensity, and character of the sounds given to the phonograph, and which are 

 reproduced with remarkable fidelity. The number of marks in a given time 

 determines pitch ; the depth of the marks, amplitude or loudness ; and the 

 character or form of the mark, to the character or quality of tone. These 

 marks can now be carefully traced and analysed. 1 



Resonance. The principle of resonance is of great importance, 

 both as explaining the mode of working of resonators employed in the 

 analysis of compound tones, and as suggesting the probable mode of 

 action of the cochlea. The material systems with which we have to do 

 in this question may be subjected to various modes of vibration, all or 

 any of which may coexist at any particular moment. Thus a system 

 may show free or forced vibrations. The period of a free vibration 

 depends on the constitution of the system itself ; the vibration is that 

 made by the system when disturbed from the position of equilibrium 

 and left to itself. A forced vibration, on the other hand, has a period 

 determined solely by the external force acting on the system. So long 

 as the external force acts, the forced vibration continues, but a free 

 vibration quickly dies away. Further, a vibrating system of one degree 

 of freedom may have the amplitude of its movements reduced by damp- 

 ing. Damping will soon extinguish a free vibration, and its influence 

 is felt on a forced vibration, when there is an approach to isochronism. 

 Now, when a forced vibration is excited in any one part of a system, all 

 the other parts are also influenced, and a vibration of the same period is 

 excited, whose amplitude depends on the constitution of the system as a 

 whole. 2 If a part of the system is specially affected within a certain 

 limit of amplitude, it is in the position of a system having one degree of 

 freedom acted on by a given force and independent of the natural 

 period. Eesonance usually occurs when there is an approximate equality 

 of periods between the vibrating body and the resonator. In some cases, 

 the amplitude within which resonance is possible may be considerable ; in 

 others, very small ; and much depends, as regards delicacy of resonance, 

 on the degree of damping that may be called into play. The best 

 example of resonance may be given by taking two forks in perfect 

 unison, say two forks, ut ; then, when one fork is bowed, the other, placed 

 in any part of the room, will respond ; while a slight change of pitch (pro- 

 duced by fixing a slider on the limb of one of the forks) will prevent 

 response, even although the deviation from unison may cause only one 

 beat per second. Tuning-forks are susceptible of sympathetic vibration 

 to a remarkable degree, notwithstanding the difficulty of setting their 

 mass in motion, because they admit of a long accumulation of minute 

 impulses ; but for this reason there must be precise agreement between 

 the pitches of the two forks. It is also observed that, if a fork is thus 

 set agoing, it continues sounding for a considerable time. On the other 

 hand, stretched membranes or strings give forth tones that rapidly 

 diminish in intensity, and they are readily set into sympathetic vibra- 

 tion, which, however, is not limited to a particular pitch. Consequently, 

 such bodies may be influenced by several tones. If a body has a 

 vibration that dies away quickly, say after 8 or 10 vibs., it is not 

 necessary that the next impulses acting upon it should be of exactly 

 the same period as those producing the first movement. 



1 See "Voice Production" in the following article of this volume, also the references 

 therein given. 



2 Rayleigh, op. cit., vol. i. p. 70. 



