A metal wire of diameter `1 mm` is held on two knife edges by a distance `50 cm`. The tension in the wire is `100 N`. The wire vibrating with its fundamental frequency and a vibrating tuning fork together produce `5 beats//s`. The tension in the wire is then reduced to `81 N`. When the two are excited, beats are heard at the same rate. Calculate
(a) frequency of a fork and
(b) the density of material of wire.
