408 



BELL SYSTEM TECHMCAL JOEKXAL 



of the cord are negligibly small the wave motion will be approximately that 

 of stationary waves as in Fig. 2. The direct waves coming from the tuning 

 fork and the reflected waves coming from the fixed point D will have nearly 

 equal amphtudes and by their interference form approximately stationary 

 waves. If, however, the frictional resistances are not negligibly small, then 

 there will be dissipation of the propagated wave energy. Hence, the direct 

 and the reflected waves will not result in stationary waves. The attenua- 

 tion of the wave is represented graphically in Fig. 3. Experiment will show 

 that, other things being equal, increased density of the string will diminish 

 attenuation, because a larger wave requires a smaller velocity in order to 

 store up a given quantity of kinetic energy and a smaller velocity brings 



^ 



I 



(1) 



Figs. 1 to ,1 — Stanfline; waves and damped waves on a mechanical transmission line 

 (taken from Pupin's paper) 



with it a smaller frictional loss. This is a striking mechanical illustration 

 of a wave conductor of high inductance. It should be observed here that 

 an increase of the density will shorten the wave-length. 



"Suppose now that we attach a weight, say a ball of beeswax, at the middle 

 point of the string, in order to increase the vibrating mass. This weight 

 will become a source of reflection and less wave energy will reach the point I) 

 than before. The efliciency of transmission will be smaller now than before 

 the weight was attached. Subdivide now the beeswax into three equal 

 parts and place them at three equidistant points along the cord. The 

 efficiency of wave transmission will be better now than it was when all the 

 wax was concentrated at a single point. By subdividing still further the 

 efflciency will be still more improved; but a point is soon reached when 



