CONTEMPORARY ADVANCES IN PHYSICS 181 



Stationary Waves and Oscillating Particles 



We have tried out, separately and in tandem, two alternative ways 

 of interpreting a beam of radiation advancing through space; first as a 

 stream of corpuscles, then as a train of waves. We will now try out 

 two alternative ways of interpreting radiation enclosed in a box; first 

 as a system of stationary waves, then as a quantity of corpuscles rush- 

 ing to and fro and bouncing from the walls. To simplify the case as 

 much as possible, think only of motions parallel to one side of the box; 

 or to make the pictures more graphic, think of a tube or pipe like those 

 often used in experiments on sound, in which the waves travel along the 

 axis. 



Now it is well known that when a train of sound-waves is sent 

 through a tube, or generated by vibrations somewhere in the tube, it is 

 partially reflected from the far end, then again partially reflected from 

 the near end, and so on over and over again; the overlapping wave 

 trains passing to and fro interfere with one another; and when the 

 wave-length is related in a certain way to the length of the tube, the 

 overlapping wave trains form a stationary ivave-pattern of alternating 

 loops and nodes — the tube is said to be in resonance. If the two ends 

 of the tube are alike (both open, or both closed) so that reflection takes 

 place in the same way as both, the waves which admit of resonance 

 are those of which the half-wave-length or an integer number of half- 

 wave-lengths fits exactly into the tube; denoting by d the length of the 

 tube, these wave-lengths are given by the formula-: 



wQj= d, n= 1,2,3, . . . (41) 



This equation defines what may be called the characteristic wave- 

 lengths of the tube. The tube distinguishes these, or the wave trains 

 possessing these wave-lengths, from all the others. 



Suppose on the other hand we had particles rushing back and forth 

 along the axis of the tube, and rebounding without loss of energy 

 whenever they struck either wall. Denote by ii the speed of a particle ; 

 it takes a time-interval Id/u to describe a complete round-trip with 

 two rebounds, and one might say crudely that it has a frequency u/ld. 

 I say "crudely" because the corpuscle is not moving with a sinusoidal 

 motion, like a pendulum-bob; its speed does not vary as a sine-function 



wave-speed and momentum. However the two relate to entirely different situations. 

 The first is a comparison between wave-speeds and corpuscle-speeds for different 

 beams in the same medium. The second is a comparison between wave-speeds and 

 corpuscle-momenta for the same beam in different media. The resemblance between 

 the two is accidental and misleadin;^. 



I am ind(-l)ted to Professors C. 11. lukarl and E. C. Kemblc for elucidation of liiis 

 point. 



