A uniform tube of length 60.5,cm is held vert | vedclass

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

Question

(D) For a resonance tube,the resonance condition is $L + e = (2n-1) \frac{\lambda}{4}$,where $e$ is the end correction.Given $L_1 = 16\,cm$ and $L_2 =

Vedclass · Accepted Answer

$272, 544$

Vedclass · Answer

(D) For a resonance tube,the resonance condition is $L + e = (2n-1) \frac{\lambda}{4}$,where $e$ is the end correction.Given $L_1 = 16\,cm$ and $L_2 = 50\,cm$ for $f = 500\,Hz$.$L_2 - L_1 = \frac{\lambda}{2} \implies 50 - 16 = 34\,cm = \frac{\lambda}{2} \implies \lambda = 68\,cm = 0.68\,m$.Speed of sound $v = f \lambda = 500 	imes 0.68 = 340\,m/s$.Now,$L_1 + e = \frac{\lambda}{4} \implies 16 + e = \frac{68}{4} = 17 \implies e = 1\,cm = 0.01\,m$.When the tube is taken out of water,it acts as an open organ pipe of length $L = 60.5\,cm + 2e = 60.5 + 2(1) = 62.5\,cm = 0.625\,m$.The resonant frequencies of an open pipe are $f_n = \frac{n v}{2L}$.For $n=1$,$f_1 = \frac{340}{2 	imes 0.625} = \frac{340}{1.25} = 272\,Hz$.For $n=2$,$f_2 = 2 	imes f_1 = 544\,Hz$.

Similar Questions

$A$ pipe $20 \; cm$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a $430 \; Hz$ source? Will the same source be in resonance with the pipe if both ends are open? (Speed of sound in air is $340 \; m/s$).

$A$ pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to

An organ pipe has a fundamental frequency of $80 \ Hz$. If one end of the pipe is closed,what are the frequencies produced? (Neglect end correction)

If we study the vibration of a pipe open at both ends,then the following statement is not true.

The length of an open organ pipe is $0.5\, m$. Calculate the fundamental frequency of the pipe,if the velocity of sound in air is $350\, m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module