The fundamental frequency of a closed organ p | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $L_1$ be the length of the closed organ pipe and $L_2$ be the length of the open organ pipe.The fundamental frequency of a closed organ pipe i

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(D) Let $L_1$ be the length of the closed organ pipe and $L_2$ be the length of the open organ pipe.The fundamental frequency of a closed organ pipe is given by $f_c = \frac{v}{4L_1}$.The frequencies of an open organ pipe are given by $f_n = \frac{nv}{2L_2}$, where $n = 1, 2, 3, ...$.The first overtone of an open organ pipe corresponds to $n = 2$, so $f_{o1} = \frac{2v}{2L_2} = \frac{v}{L_2}$.According to the problem, the fundamental frequency of the closed pipe is equal to the first overtone frequency of the open pipe:$f_c = f_{o1}$$\frac{v}{4L_1} = \frac{v}{L_2}$$L_2 = 4L_1$Given $L_2 = 60 \,cm$, we have:$60 \,cm = 4L_1$$L_1 = \frac{60}{4} \,cm = 15 \,cm$.Therefore, the length of the closed pipe is $15 \,cm$.

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of the open pipe is $60 \,cm$, the length of the closed pipe will be: (in $\,cm$)

Similar Questions

It is desired to increase the fundamental resonance frequency in a tube which is closed at one end. This can be achieved by

Two consecutive harmonics of an air column in a pipe closed at one end are of frequencies $150 \,Hz$ and $250 \,Hz$. The fundamental frequency of the air column is: (in $\,Hz$)

Two closed organ pipes,when sounded simultaneously,give $4$ beats per second. If the longer pipe has a length of $1 \ m$,then the length of the shorter pipe will be,... $cm$ $(v = 300 \ m/s)$.

The stationary wave $y = 2a \sin kx \cos \omega t$ in a closed organ pipe is the result of the superposition of $y = a \sin (\omega t - kx)$ and

$A$ cylindrical tube,open at both ends,has a fundamental frequency $f_0$ in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is

Vedclass Test Series

Exam Paper Generator

Online Exam Module