Let the frequency of tuning fork be N
As the frequency of vibration string∝1/length of string
- For sonometer wire of length 40cm,frequency must be (N+5) and that for the sonometer wire of length 44 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) × 40 = (N−5) × 44
⇒ 40 N + 200 = 44 N - 220
⇒ 40 N - 44 N = -220 - 200
⇒ - 4 N = - 420
⇒N = 420/4
N = 105 Hz