Question

A glass tube 1.5 m long and open at both ends, is immersed vertically in a water tank completely. A tuning fork of frequency 660 Hz is vibrated. It is 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 totally comes out of water is (velocity of sound in air $=330m{s}^{-1}$) :

• A. 12
• B. 6
• C. 8
• D. 4

Answer 1

Answer: (B)

6

Given, $L=1.5m,f=660Hz,\&v=330m{s}^{-1}$

A both end open organ pipe immersed in water will act as a closed organ pipe.

Let us suppose that the total number of resonances that occurred before the tube came completely out of water is $N$

We have,

$f=\frac{(2N-1)v}{4L}$ (only odd harmonics in closed organ pipe)

$2N-1=\frac{4fL}{v}$

$N=\frac{\frac{4fL}{v}+1}{2}$

$N=\frac{4fL+2v}{2v}$

Putting values,

$N=\frac{4\times 660\times 1.5+2\times 330}{2\times 330}$

$N=\frac{3960}{660}=6$

So, B is the correct answer.