Question

The fundamental frequency of an open organ pipe is $n$. The pipe is vertically immersed in water such that half of its length is submerged. The fundamental frequency of air column in this position will be

• A. $n/3$
• B. $n/2$
• C. $n$
• D. $2n$

Answer 1

The correct option is C $n$

Let velocity of sound in air be $v.$

Open organ pipe:

Let Length of the pipe be $L$.

Fundamental frequency i.e $m=1$, ${\nu }_1=n=\frac{v}{2L}$

When the pipe is immersed in water, it acts like a closed organ pipe.

Length of the air column, $l=\frac{L}{2}$

Frequency of different modes in closed organ pipe, ${\nu }_p^{\prime }=\frac{(2p-1)v}{4l}$

Fundamental frequency i.e $p=1$ , ${\nu }_1^{\prime }=\frac{v}{4\times \frac{L}{2}}=\frac{v}{2L}=n$