The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is increased by 69 % , keeping the length constant. The frequency of the wire is

Step-by-step solution

We know that, frequency of vibration of a stretched string is given by v = 1 2 l T m where, T = tension in string m = mass /length and l = length of string. New frequency, v ' = v + 9 = 1 2 l T + 69 / 100 T m ⇒ v v ' = T 169 100 T ⇒ v v + 9 = 100 169 = 10 13 ⇒ 13 v = 10 v + 90 v = 30 H z