# An open pipe is in resonance in $2^{nd}$ harmonic with frequency ${f_1}$ . Now one end of the tube is closed and frequency is increased ${f_2}$ such that the resonance again occurs in ${n^{th}}$ harmonic. Choose the correct option .

A. $n = 3;{f_2} = \dfrac{{3{f_1}}}{4}$

B. $n = 3;{f_2} = \dfrac{{5{f_1}}}{4}$

C. $n = 5;{f_2} = \dfrac{{3{f_1}}}{4}$

D. $n = 5;{f_2} = \dfrac{{5{f_1}}}{4}$

Last updated date: 25th Jan 2023

•

Total views: 171.3k

•

Views today: 4.65k

Answer

Verified

171.3k+ views

**Hint:**Here we are given two types of pipe, open and closed. We are given at first that the pipe is open and after that as its face is closed, it becomes a closed pipe. We need to know the formula to find the frequency of the open and closed pipe. It is seen that resonance occurs at a harmonic, thus we can find the frequency and match with answers.

**Complete step by step answer:**

Let the speed of sound in air be $v$ and the length of the pipe be $l$. Thus, for an open pipe we know the frequency of second harmonic is given by:

$\dfrac{{nv}}{{2l}}$ , here n = 2 , hence ${f_1} = \dfrac{v}{l} - - - - (1)$ .

Now as its one end is closed it becomes a closed pipe, thus the formula for the ${n^{th}}$ frequency of a closed pipe ${f_2} = \dfrac{{(2n - 1)v}}{{4l}} . - - - - (2)$

Taking the relation from equation (1), equation (2) will be

${f_2} = \dfrac{{(2n - 1){f_1}}}{4} - - - - (3)$ .

Thus we now have the required value, now we just have to place the value as indicated in the question and get the required values . Let us put n = $3$ in the equation, thus we get ${f_2} = \dfrac{{(2n - 1){f_1}}}{4}$ , thus ${f_2} = \dfrac{{5{f_1}}}{4}$.

Now let us put $n = 5$ in the equation, thus we get ${f_2} = \dfrac{{9{f_1}}}{4}$.

**Hence (B) is the correct option.**

**Note:**It is important to remember the formula of frequency for an open and a closed pipe. Also remember that an open pipe can be converted to a closed pipe by closing the other end, or by placing the other end in water.

Recently Updated Pages

Which element possesses the biggest atomic radii A class 11 chemistry JEE_Main

The highly efficient method of obtaining beryllium class 11 chemistry JEE_Main

Which of the following sulphates has the highest solubility class 11 chemistry JEE_Main

Amongst the metal Be Mg Ca and Sr of group 2 of the class 11 chemistry JEE_Main

Which of the following metals is present in the greencolored class 11 chemistry JEE_Main

To prevent magnesium from oxidation in the electrolytic class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

What is the difference between anaerobic aerobic respiration class 10 biology CBSE