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

Since frequency, `v prop sqrt((T)/(m))`
when `m = pi r^(2) rho`
So in first case, `v prop sqrt((T)/(pi r^(2) rho))`
or `v prop (1)/(r) sqrt((T)/(pi rho))`
In second case `v' = (1)/(3r) sqrt((T)/(pi rho)) = (1)/(3) v`
i.e. the frequency will change by a factor `(1)/(3)`