A sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same, by what factor will the frequency change ?

Explanation

Frequency of vibarations produced by a stretched wire
`" " v=(n)/(2l)sqrt((T)/(mu))`
Mass per unit length `mu=("Mass")/("Length")=(pir^(2)lrho)/(l)=pir^(2)rho" " [ :. M=vp=Alrho=pir^(2)lrho]`
`:. " " v=(n)/(2l)sqrt((T)/(pir^(2)rho))rArrvpropsqrt((1)/(r^(2))`
`" " vprop (1)/(r)`
Hence , when radius is tripled , v will be `(1)/(3)` rd of previous value .