Question

A tuning fork produces 5beats per sec with a sonometer of lengths 40com and 44 cm the frequency is

Answer 1

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