A tuning fork gives 3 beats with 50 ~cm length of sonometer wire. If the length of the wire is shortened by 1 ~cm , the number of beats is still the same. The frequency of the fork is

Step-by-step solution

The frequency of a vibrating wire f = 1 2 l T m f 1 l fl = constant Let the frequency of the fork be f and the initial and final frequencies of the wire be f₁ and f₂ . The number of beats heard before decreasing the length is f-f₁=3 The number of beats after decreasing the length is f ₂- f =3 array ll & f ₁ l₁= f ₂ l₂ & ( f -3) 50=( f +3) 49 & 50 f -49 f =147+150 & f =297 ~Hz array