The fundamental frequency of a sonometer wire increases by6 Hz if its tension is increased by44 % , keeping the length constant . Find the change in the fundamental frequency of the sonometer wire when the length of the wire is increased by 20 % , keeping the original tension in the wire constant.

The fundamental frequency of a sonometer wire increases by6 Hz if its

1.	The fundamental frequency of a sonometer wire increases by6 Hz if its tension is increased by44 % , keeping the length constant . Find the change in the fundamental frequency of the sonometer wire when the length of the wire is increased by 20 % , keeping the original tension in the wire constant.
Answer» Solution :Fundamental frequency of vibrations of string ` n = (1)/( 2 L) SQRT ((T)/(m))` At constant length , `n PROP sqrt(T) or (n)/ ( sqrt(T)) = constant` i. New tension , `T' = T + ( 44)/( 100) T = 1.44 T` If `n'` is new frequency , then `(n')/(sqrt( T')) = (n) /( sqrt(T))` ` n' = ( sqrt ((T')/(T)))n`(ii) ` :.n' = n + 6 ` From Eq. (iii) ` n + 6 = ( sqrt((1.44 T)/(T)))n` or ` n + 6 = 1.2 n` ` 0.2 n = 6 or n = (6)/( 0.2) = 30 Hz` ii.As tension is constant ` n prop (1)/(l) or nl = constant `(iii) When length increase by ` 20%` New length ` l' = l + (20)/( 100) l = 1.2 l` As ` nl= constant ` Therefore , ` nl = n' l'` ` n' = (l)/( l') n = (l)/( 1.2 l) xx 30 = 25 Hz` Change in fundamental frequency ` Delta n =n' - n = 25 - 30 = - 5 Hz` Therefore , ` DELTAN = 5 Hz( decrease)`