An open and a closed organ pipe have the same | vedclass

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

Question

(D) For an open organ pipe of length $\ell$,the frequency of the $p^{th}$ mode is given by $f_{open} = p \frac{v}{2\ell}$,where $v$ is the speed of so

Vedclass · Accepted Answer

$\frac{2p}{2p - 1}$

Vedclass · Answer

(D) For an open organ pipe of length $\ell$,the frequency of the $p^{th}$ mode is given by $f_{open} = p \frac{v}{2\ell}$,where $v$ is the speed of sound.For a closed organ pipe of length $\ell$,the frequency of the $p^{th}$ mode (where $p$ is the harmonic number) is given by $f_{closed} = (2p - 1) \frac{v}{4\ell}$.To find the ratio of the $p^{th}$ mode frequency of the open pipe to the closed pipe,we divide the two expressions:$\frac{f_{open}}{f_{closed}} = \frac{p \frac{v}{2\ell}}{(2p - 1) \frac{v}{4\ell}}$Simplifying the expression:$\frac{f_{open}}{f_{closed}} = \frac{p}{2\ell} 	imes \frac{4\ell}{2p - 1} = \frac{2p}{2p - 1}$Thus,the ratio is $\frac{2p}{2p - 1}$.

An open and a closed organ pipe have the same length. The ratio of the $p^{th}$ mode of frequency of vibration of the two pipes is

Similar Questions

In the fundamental mode,the time required for a sound wave to travel from the open end to the closed end of an air-filled pipe is $t$ seconds. What is the frequency of vibration of the air column? (Neglect end correction)

For a certain organ pipe,three successive resonance frequencies are observed at $425 \, Hz, 595 \, Hz,$ and $765 \, Hz$ respectively. Taking the speed of sound in air to be $340 \, m/s$,the fundamental frequency of the pipe (in $Hz$) is:

An open pipe of length $l$ vibrates in its fundamental mode. The pressure variation is maximum at

$A$ tuning fork of frequency $500 \ Hz$ is sounded on a resonance tube. The first and second resonance are obtained at $17 \ cm$ and $52 \ cm$. The velocity of sound is $........ \ m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module