The vibrations of four air columns under identical conditions are represented in the figure below. The ratio of frequencies np: nq: nr: ns will be

Question

The vibrations of four air columns under identical conditions are represented in the figure below. The ratio of frequencies np: nq: nr: ns will be (A) 12: 6: 3: 4 (B) 1: 2: 4: 3 (C) 4: 2: 3: 1 (D) 6: 2: 3: 4

Tardigrade Admin · Accepted Answer

P, S, will be 1 text st and 2 text nd harmonics of closed tube. P=(v/4 l), S=(v/4 l) Q, R are the 1 text st and 2 text nd harmonics of open pipe. Q=(v/2 l), R=(v/l) ∴ P: Q: R: S=1: 2: 4: 3

Q. The vibrations of four air columns under identical conditions are represented in the figure below. The ratio of frequencies $n_{p} : n_{q} : n_{r} : n_{s}$ will be

12 : 6 : 3 : 4

1 : 2 : 4 : 3

4 : 2 : 3 : 1

6 : 2 : 3 : 4

$P, S$ , will be $1^{st}$ and $2^{nd}$ harmonics of closed tube.
$P = \frac{v}{4 l}, S = \frac{v}{4 l}$
$Q, R$ are the $1^{st}$ and $2^{nd}$ harmonics of open pipe.
$Q = \frac{v}{2 l}, R = \frac{v}{l}$
$∴ P : Q : R : S = 1 : 2 : 4 : 3$

Q. The vibrations of four air columns under identical conditions are represented in the figure below. The ratio of frequencies np​:nq​:nr​:ns​ will be