Internal Friction on Resonance. 



181 



An expression for this could of course be at once written 

 down without approximation; but the case where k is small 

 is most important ; then we have 



I ~ nl nHk 



L Q=cos — • — -, 

 v a 2a 



r a A 



sin — 

 a 



A cos 



nl 



B,= 



sin' 



nHk 



nl 2a 



unless sin — becomes very small, 

 a J 



r 



<£ = A 



. nx 

 sin — 

 a 



nl 



sin 



, A kri 1 f. nl . nx 



vr= . • — < I cos — , sin — 



• m.l. V.n I n n 



,nt 

 sin* — 

 a 



\a L 



L 



nx . nl 

 — x cos — sin — 

 « a 





Work done on the string 



?2 8 E/£ 



4« sin 2 



-A 



nl n 



nl . nl 



I cos^ — • cos — sin — 



a a a a 



a 



, jTi . 2 nl . nl nl\ 



+ /- sin 44 f-* sin— cos — r 



a a a a ) 



n^tkh? \nl 



Aa sin 2 



? \nl - . w/ ra/1 

 -,i — r sin- cos- \ . 

 w« I a a a ) 



