The lengths of two open organ pipes are l and | vedclass

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

Question

(C) For an open organ pipe of length $L$,the fundamental frequency is given by $n = \frac{v}{2L}$.For the first pipe of length $l$,the frequency is $n

Vedclass · Accepted Answer

$\frac{v \Delta l}{2l^2}$

Vedclass · Answer

(C) For an open organ pipe of length $L$,the fundamental frequency is given by $n = \frac{v}{2L}$.For the first pipe of length $l$,the frequency is $n_1 = \frac{v}{2l}$.For the second pipe of length $(l + \Delta l)$,the frequency is $n_2 = \frac{v}{2(l + \Delta l)}$.The beat frequency is the difference between the two frequencies: $f_{beat} = n_1 - n_2 = \frac{v}{2l} - \frac{v}{2(l + \Delta l)}$.Taking $\frac{v}{2}$ as a common factor: $f_{beat} = \frac{v}{2} \left( \frac{1}{l} - \frac{1}{l + \Delta l} \right)$.Simplifying the expression: $f_{beat} = \frac{v}{2} \left( \frac{l + \Delta l - l}{l(l + \Delta l)} \right) = \frac{v \Delta l}{2l(l + \Delta l)}$.Since $\Delta l$ is very small compared to $l$,we can approximate $l + \Delta l \approx l$.Therefore,$f_{beat} \approx \frac{v \Delta l}{2l^2}$.

The lengths of two open organ pipes are $l$ and $(l + \Delta l)$ respectively. Neglecting end correction,the frequency of beats between them will be approximately (Here $v$ is the speed of sound).

Similar Questions

The fundamental frequency of a closed pipe is $220 \ Hz$. If $\frac{1}{4}$ of the pipe is filled with water,the frequency of the first overtone of the pipe now is ..... $Hz$.

$A$ pipe $17 \, cm$ long is closed at one end. Which harmonic mode of the pipe resonates with a $1.5 \, kHz$ source? (Speed of sound in air $= 340 \, m \, s^{-1}$)

An air column in a pipe,which is closed at one end,will be in resonance with a vibrating tuning fork of frequency $264 \,Hz$ for various lengths. Which one of the following lengths is not possible (in $\,cm$)? $(V=330 \,m/s)$

In a $1 \ m$ long open pipe,what is the harmonic of resonance obtained with a tuning fork of frequency $480 \ Hz$? (Assume the speed of sound $v = 330 \ m/s$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module