Important points:

(1) As a string has several natural frequencies, so when it is excited with a tuning fork, the string will be in resonance with the given object if any of its natural frequencies coincides with the object.

(2)  (i) n ∝ 1/T if T and m are constant (ii) n ∝ √T   if L and m are constant (iii) n ∝ √(1/m)  if T and L are constant

(3) If M is the mass of the string of length L,m = M/L

            So      n = 1/2L √(T/m) = 1/2L √{T/(M/L)} =1/2 √(T/ML) = 1/2L √(T/πr²ρ)   

            where m = πr²ρ  (r = Radius,  ρ = Density) 

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