A closed and an open organ pipe have the same | vedclass

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

Question

(C) For a closed organ pipe,the frequency of the $n$-th overtone is given by $f_{c} = (2n + 1) \frac{v}{4\ell}$,where $n$ is the overtone number.For t

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(C) For a closed organ pipe,the frequency of the $n$-th overtone is given by $f_{c} = (2n + 1) \frac{v}{4\ell}$,where $n$ is the overtone number.For the $7$-th overtone $(n=7)$,$f_{c} = (2 	imes 7 + 1) \frac{v}{4\ell} = \frac{15v}{4\ell}$.For an open organ pipe,the frequency of the $n$-th overtone is given by $f_{o} = (n + 1) \frac{v}{2\ell}$.For the $7$-th overtone $(n=7)$,$f_{o} = (7 + 1) \frac{v}{2\ell} = \frac{8v}{2\ell} = \frac{4v}{\ell} = \frac{16v}{4\ell}$.The ratio of the frequencies is $\frac{f_{c}}{f_{o}} = \frac{15v/4\ell}{16v/4\ell} = \frac{15}{16}$.Given the ratio is $\left(\frac{a-1}{a}ight) = \frac{15}{16}$,comparing the terms,we get $a = 16$.

$A$ closed and an open organ pipe have the same lengths. If the ratio of the frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$,then the value of $a$ is:

Similar Questions

An air column in a pipe,which is closed at one end,will be in resonance with a vibrating tuning fork of frequency $264 \, Hz$ if the length of the column in $cm$ is (velocity of sound $= 330 \, m/s$)

$A$ pipe $20$ $cm$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of $1237.5$ $Hz$? (Speed of sound in air $= 330$ $m/s$).

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed organ pipe $L$ metre long. The length of the open pipe will be:

$A$ closed pipe and an open pipe have their first overtone equal in frequency. Then the lengths of these pipes are in the ratio

$A$ pipe of length $85\, cm$ is closed from one end. Find the number of possible natural oscillations of the air column in the pipe whose frequencies lie below $1250\, Hz$. The velocity of sound in air is $340\, m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module