Two tuning forks A and B sounded together give 6 beats per second. With an air resonance tube closed at one end, the two forks give resonance when the two air columns are 24 ~cm and 25 cm respectively. Calculate the frequencies of forks.

Step-by-step solution

Let the frequency of the first fork be f ₁ and that of second be f ₂ We then have, f ₁= v 4 24 and f ₂= v 4 25 We also see that f ₁> f ₂ f ₁- f ₂=6 and f ₁ f ₂ = 24 25 Solving (i) and (ii), we get f ₁=150 ~Hz and f ₂=144 ~Hz