132 DYNAMICAL THEOKY OF SOUND 



Theory and observation alike shew that the effect of curving 

 a bar is to lower the pitch of the gravest mode and to make the 

 nodes approach the centre. It was found by Chladni that 

 when the bar takes the form of an elongated U, the nodes are 

 very close to the bend. The amplitude of vibration at the 

 centre of the bend will therefore be small compared with that 

 at the end of the prongs. The circumstances are somewhat 

 modified by the attachment of the stem, but the transmission 

 of energy is comparatively slow, and the vibrations have con- 

 siderable persistence. A fork may also be compared to a couple 

 of bars each clamped at one end, and the formula (2) of 46, 

 with ml/7r = '59686, may be used to estimate the frequency 

 theoretically. If this analogy were exact there would of course 

 be no loss of energy of the kind just referred to. 



Massive forks are usually set into vibration by means of 

 a violoncello bow applied to one prong near the free end. The 

 production of overtones having nodes in this neighbourhood is 

 thus discouraged. The fundamental is further reinforced re- 

 latively to the other modes if the stem be screwed into the 

 upper face of a resonance box of suitable dimensions. 



When a fork is excited in this or in other ways, it often 

 happens that the motion is not in the first instance symmetrical 

 with respect to the medial plane. In that event the vibration 

 may be regarded as made up of a symmetrical and an unsym- 

 metrical component. These will in general have slightly 

 different frequencies, and beats may be produced. But unless 

 the stem be very firmly fixed the vibrations of the latter class 

 are rapidly dissipated by being communicated to the support, 

 since they involve an oscillation of the centre of mass of the 

 fork. 



The first overtone of a fork may be elicited in considerable 

 intensity by bowing one of the prongs near the bend ; the note 

 produced is very shrill. 



50. Effect of Permanent Tension. 



In the theory developed in 45 it was assumed that the 

 longitudinal tension, when integrated over the area of the 

 cross-section, vanishes. It is easy to see that the effect of 



