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other to the right. The dynamical deviations occurring in reality 
move with the same velocity as the wave §,, which they must 
disturb! Considered in this light we cannot expect at all that the 
replacing of the dynamical deviations by statical deviations will bring 
about anything useful. 
Consequently the deviation &, we introduced before has also to 
be a progessive wave, and we should examine the interaction of 
two progressive waves §, and §,, in either case they run along 
the bar in a different or in the same direction. 
For this examination the equation of motion (9), where P= 0, 
can be used. For the sake of brevity we shall take formuia (1). 
Once more we put S=8, +8 +8, The waves 5, and § now 
satisfy each separately (1), so that for §, we have: 
DE, OS, (EE ae, OS, = 
Of dz,  \ dr Ow? | Ox de? oe 
Just as with the statical deviations we may neglect the terms 
with « in the equations §, and &. When we introduce the new 
variables 
ue dt mn 7 
then we can represent two waves moving in the same direction by 
En ait, (v) 5. Us (v). 
After transformation (11) becomes: 
0°5, 
Ou Ov et: 
Integrating this first over v and afterwards over w we find 
2 PN elen 
4 (7 oJ 1 “irk ws 0): 
=F ONO+FAMFhO 
whereby the functions f, and f, can be used to satisfy the initial 
conditions. When these conditions are that & and — will be 
& 
zero for {= 0, then we find 
PAS ie 4 
5 5 oC), ©). 
From this follows that the two waves §, and 5, really react 
on each other and produce a secondary wave increasing with ¢ — 
that is to say if f, and # cover each other, not if they are 
two finite waves following each other. If one takes the 
special case of sine-waves, then §, becomes a “combination-wave”, 
consisting of two terms, with the sum and the difference of the 
frequencies of =, and &,. However, what is in the first place impor- 
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