A tuning fork vibrating with a sonometer having 20 cm wire produces 5 beats per second. The beat frequency does not change if the length of the wire is changed to 21 cm. the frequency of the tuning fork (in Hertz) must be

Let the frequency of  tuning fork be NAs the frequency of vibration string ∝ 1length of stringFor sonometer wire of length 20 cm, frequency must be (N + 5) and that for the sonometer wire of length 21 cm, the frequency must be (N- 5) as in each case the tuning fork produces 5 beats/sec with sonometer wire.Hence n1I1 = n2I2  ⇒ (N+5)×20 = (N-5)×21⇒N = 205 Hz