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A wire of uniform cross-section is stret...

A wire of uniform cross-section is stretched between two points `100cm` apart. The wire is fixed at one end and a weight is hung over a pulley at the other end. A weight of 9kg produces a fundamental frequency of `750Hz`.
(a) What is the velocity of the wave in wire?
(b) If the weight is reduced to `4kg`, what is the velocity of wave?

Text Solution

Verified by Experts

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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