Question

A glass tube $1.5m$ long and open at both ends, is immersed vertically in a water tank completely. A tuning fork of $660Hz$ is vibrated and kept at the upper end of the tube and the tube is gradually raised out of water. The total number of resonances heard before the tube comes out of water, taking velocity of sound in air $330m/$sec is

• A. $4$
• B. $8$
• C. $6$
• D. $12$

Answer 1

The correct option is C $6$

A glass tube open at both ends and the length $l=1.5m$
Frequency of tuning fork $n=660Hz$
velocity of sound in air $v=330m/$sec

Suppose $N$ resonance occurred before coming out, modes of vibration in a closed pipe,

$\Rightarrow n=\frac{(2N-1)v}{4L}$

$\Rightarrow l=\frac{(2N-1)v}{4n}$

$\Rightarrow 1.5m=\frac{(2N-1)\times 330\frac{m}{s}}{4\times 660Hz}$

$\Rightarrow (2N-1)=8\times 1.5$

$\Rightarrow N\approx 6$

Final Answer: (b)