An open pipe is suddenly closed at one end wi | vedclass

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

Question

(D) Let the length of the pipe be $l$ and the speed of sound be $v$.The fundamental frequency of an open organ pipe is given by $f_{open} = \frac{v}{2

Vedclass · Accepted Answer

$200$

Vedclass · Answer

(D) Let the length of the pipe be $l$ and the speed of sound be $v$.The fundamental frequency of an open organ pipe is given by $f_{open} = \frac{v}{2l}$.The frequencies of a closed organ pipe are given by $f_n = \frac{nv}{4l}$,where $n$ is an odd integer $(n = 1, 3, 5, ...)$.The third harmonic of a closed pipe corresponds to $n = 3$,so $f_{closed, 3} = \frac{3v}{4l}$.According to the problem,the frequency of the third harmonic of the closed pipe is $100 \ Hz$ higher than the fundamental frequency of the open pipe:$f_{closed, 3} = f_{open} + 100$Substituting the expressions:$\frac{3v}{4l} = \frac{v}{2l} + 100$Rearranging the terms:$\frac{3v}{4l} - \frac{2v}{4l} = 100$$\frac{v}{4l} = 100$We need to find the fundamental frequency of the open pipe,which is $f_{open} = \frac{v}{2l}$.Since $\frac{v}{4l} = 100$,then $\frac{v}{2l} = 2 	imes 100 = 200 \ Hz$.

An open pipe is suddenly closed at one end with the result that the frequency of the third harmonic of the closed pipe is found to be higher by $100 \ Hz$ than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is .... $Hz$.

Similar Questions

$n_{1}$ is the frequency of a pipe closed at one end and $n_{2}$ is the frequency of a pipe open at both ends. If both are joined end to end,find the fundamental frequency of the closed pipe so formed.

In the experiment to determine the speed of sound using a resonance column, which of the following statements is correct?

An organ pipe of length $L$ open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of $480 \ Hz$. What should be the length of a pipe closed at one end,so that it also vibrates in its first harmonic with the same tuning fork?

Vedclass Test Series

Exam Paper Generator

Online Exam Module