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. $\dfrac{n}{3}$
B. $\dfrac{n}{2}$
C. $n$
D. $2n$

Answer 1

In order to answer this question, to find the fundamental frequency of the air column, first we will assume the velocity of sound as a variable and also the length of the pipe. And then we will use the formula of fundamental frequency for both open pipe and the closed pipe as well.

Formula-used:
$n = \dfrac{v}{{2L}}$
Where $v$ is speed of sound and $L$ is length of organ pipe and;
${n^1} = \dfrac{v}{4{L^1}}$
Where = half of open organ pipe = $\dfrac{L}{2}$

Complete step by step answer:
The experiment on sound waves is related to the organ pipe. There are two types: open pipe and closed pipe. An open pipe is one in which both ends are opened and sound is transferred through it. Only one end of a closed organ pipe is open, while the other is closed, allowing sound to pass through.

Now, let us now come to the question.Let velocity of sound in air be $v.$
Open organ pipe: Let Length of the pipe be $L$.
Fundamental frequency i.e. $m = 1$ , ${v_1} = n = \dfrac{v}{{2L}}$
When the pipe is immersed in water, it acts like a closed organ pipe.
Length of the air column, $l = \dfrac{L}{2}$
Frequency of different modes in closed organ pipe,
$v_p^1 = \dfrac{{\left( {2p - 1} \right)v}}{{4l}}$
Fundamental frequency i.e. $p = 1$ ,
$\therefore v_1^1 = \dfrac{v}{{4 \times \dfrac{L}{2}}} = \dfrac{v}{{2L}} = n$
Therefore, the fundamental frequency of air column in this position will be $n$ means it remains the same.

Hence, the correct option is C.

Note: The term "closed organ pipe" refers to a pipe that is blocked at one end by a solid item. If any medium denser than air is present on the opposite end, it can be deemed closed. To examine the issue and determine the parameters such as frequency and conduct the experiment, it is necessary to understand that sound waves cause standing waves inside the tube. It is recommended that students deduce these phrases on their own at least once.