Question

In a resonance tube experiment when a tuning fork of frequency 500 Hz is sounded over it, the first and second resonances are obtained at 17 cm and 52cm. the velocity of sound is

Ans is 350 m/s.

Please give detailed explanation as I won't be able to understand concise answers.

Answer 1

1^st eq. is-
l₁ = v/4f.........(1)
2^nd eq.is
l₂ = 3v/4f........(2)
Apply (2) – (1)
l₂ - l₁ = 3v/4f – v/4f = 2v/4f = v/2f
52-17 = v/ (2* 500)
35 * 1000 cm/sec
350m/sec