172 THE ROYAL SOCIETY OF CANADA 



mentioned. First, in using long bars the dust figures showed the 

 presence of overtones quite markedly and the nature of these con- 

 firmed the theory of nodes and loops in the vibrating bar as advanced 

 above. 



Secondly, for very short bars, ten cms. and less, it was found 

 very difficult at first to get any effect. The explanation was sought 

 in the theory of impact. The classical theory of impact, based upon 

 the theory of the compressional waves in the bar and the hammer 

 being reflected from the distant ends as tension waves and thrusting 

 the two pieces apart, is given in Thomson and Tait : Treatise on Natural 

 Philosophy, Part 2, pp. 228-229. If the hammer be short compared 

 with the length of the bar, it should be possible to cause the hammer 

 to rebound so as to allow the bar to vibrate freely and produce the 

 standing air waves in the tube. The size of the hammer permissible 

 can be calculated and this was done, but the hammer produced was 

 not a success. It was found that a very much smaller hammer with 

 a slender handle was required. A paper recently published by 

 Tschudi^ bears on this question. By a very precise experimental 

 method the author shows that the compressional wave theory of 

 impact does not hold, but that the theory advanced by Hertz^" better 

 represents the facts for the duration of impact of spherical bodies 

 and also for cylinders. This theory is based on the local eflfect of the 

 pressure, which seems to explain how the end of a bar becomes 

 "upset" under the blows of the hammer. Of course the compressional 

 waves also pass through the bar and are reflected from the ends as 

 well. 



It must be pointed out that the air waves arising from a vibrating 

 disc such as the end of one of these bars do not move out in a spherical 

 form if the frequency is great, but in the form of a beam whose 

 boundary makes an angle 4> with the normal to the disc through 



X 

 its centre given by the relation sin = 1.22 — 



where D is the diameter of the disc and X is the wave length of the air 

 waves produced. The angle <^ for a bar of 2.54 cms. diameter and 

 5 cms. long is 17° approx. 



Also, it can be shown that on account of wave interference, 

 efïects occur in the medium immediately in front of the disc resulting 

 in places of maximum and minimum intensity along the projected 

 axis of the bar. 



^Duration of Impact of Bars. Physical Review, p. 423, Jan., 1922. 

 i^Miscellaneous Papers, p. 146, 1896. 



