294 



THE ROYAL SOCIETY OF CANADA 



Tschudi, following the method of Hertz, has developed a mathe- 

 matical formula, involving two empirical constants which he deter- 

 mined in his experiments, giving the relation between the duration 

 of impact, velocity of approach, and length of colliding bars, in the 

 case of two circular section bars impinging end on. 



The considerations just mentioned have a bearing on the method 

 of exciting longitudinal waves in a metal bar, as described in the 

 paper by Mr. Lang^ at this meeting. The waves there are excited by 

 the impact of a hammer on the end of a metal bar clamped in the 

 middle, and some of the energy of the impact is transformed into 

 compressional waves, for their existence is easily demonstrated by 

 the "Kundt's figures" which can be produced in a tube at the far 

 end of the bar. Tschudi's formula will not exactly apply here, where 

 the bar at rest was clamped and not free, but it at least will indicate 

 the order of the time required for the duration of the impact. 



The gravest note produced by the compression will be that in 

 the clamped bar and the time of travel of this wave forward and back 

 along the bar can be calculated from the measurement of the length 

 of the Kundt's figures so produced or from the length of the bar. 

 This period, on Hertz' theory of impact, should be much less than 

 the duration of the impact, the order of which we can now calculate, 

 accepting Tschudi's results and extrapolating in his formula. 



Taking the cases of the longest and shortest bars of steel experi- 

 mented with by Mr. Lang, giving high frequency longitudinal waves 

 on impact of 1,280 to 50,000 vibrations per second, the diameter of 

 the bars being 2.54 cms., and the velocity of approach 100 cms. per 

 second, we have the following: 



Length of clamped 

 bar 



200 cms. 

 5 " 



Length of hammer 



3 cms. 

 3 " 



Period of vibration 



7.8X10-^ sees. 

 2X10-5 " 



Calculated dura- 

 tion of report 



9 X 10-* sees. 

 9X10-5 " 



It is seen that for both longest and shortest bars and very short 

 hammer the time for the duration of impact was greater than the 

 period of longitudinal vibration, though the two are approaching the 

 same value as the period of oscillation lengthens. It follows that 

 the thrust to separate hammer and bar by waves reflected from the 

 far end of the bar must always be less than the pressure created by 

 the impact until the latter disappears; and it follows also that the 

 longitudinal waves can travel back and forth in each bar, and be 



iR. J. Lang, High Frequency Vibrations and Elastic Modulus of Metal Bars. 

 Trans. Roy. Soc. Can., May, 1922. 



