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A wire of uniform cross-section is stretched berween two points I w apart. The wire is fixed at one end und u weight of 9 kg is hung over a pulley at the other end produces fundamental frequency of 750 Hz. (a) What is the velocity of transverse waves propagating in the wire ? (b) If now the suspended weight is submerged in a liquid of density (5/9) that of the weight, what will be the velocity and frequency of the waves propagating along the wire ? |
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Answer» Solution :In case of FUNDAMENTAL vibration of string `(lambda//2)=L.i.e, lambda=2xx1=2m` Now as `v=F lambda and f=750 HZ`, `V_(T)=2xx750=1500 m//s` (b) Now as in case of a wire under tension `v= sqrt((T)/(mu))` `V_(B)=1500 sqrt((T_(B))/(T_(A))) (or) 1500 sqrt((g[1-sigma//rho])/(g)=1000 m//s` so from `v=f lambda, f_(B)=(V_(B))/(lambda_(B))=(1000)/(2)=500 Hz i.e`, In this situation `lambda=2m, f=500 Hz and v=1000 m//s` 
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