A closed organ pipe of length L and an open o | vedclass

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

Question

(B) For a closed organ pipe,the first overtone is the $3^{rd}$ harmonic. The frequency is given by $f = \frac{3v_1}{4L} = \frac{3}{4L} \sqrt{\frac{1}{

Vedclass · Accepted Answer

$\frac{4 L}{3} \sqrt{\frac{\rho_1}{\rho_2}}$

Vedclass · Answer

(B) For a closed organ pipe,the first overtone is the $3^{rd}$ harmonic. The frequency is given by $f = \frac{3v_1}{4L} = \frac{3}{4L} \sqrt{\frac{1}{\beta \rho_1}}$,where $\beta$ is the compressibility.For an open organ pipe,the first overtone is the $2^{nd}$ harmonic. The frequency is given by $f = \frac{2v_2}{2L'} = \frac{v_2}{L'} = \frac{1}{L'} \sqrt{\frac{1}{\beta \rho_2}}$.Since the compressibility $\beta$ is the same for both gases,and assuming the bulk modulus $K = 1/\beta$ is the same,we equate the frequencies:$\frac{3}{4L} \sqrt{\frac{1}{\beta \rho_1}} = \frac{1}{L'} \sqrt{\frac{1}{\beta \rho_2}}$$\frac{3}{4L \sqrt{\rho_1}} = \frac{1}{L' \sqrt{\rho_2}}$$L' = \frac{4L}{3} \sqrt{\frac{\rho_1}{\rho_2}}$.

$A$ closed organ pipe of length $L$ and an open organ pipe contain gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibility of the gases is equal in both the pipes. If the frequencies of their first overtones are the same,then the length of the open organ pipe is:

Similar Questions

The frequency of a vibrating air column in a pipe,open at both ends,is $f_1$. When $\frac{3}{4}$ of its length is immersed in water,the frequency of the vibrating air column is $f_2$. The value of $\frac{f_1}{f_2}$ is

The fundamental note produced by a closed organ pipe is of frequency $f$. The fundamental note produced by an open organ pipe of the same length will be of frequency .... $(f)$

$A$ tuning fork of frequency $340\, Hz$ is vibrated just above a tube of $120\, cm$ height. Water is poured slowly into the tube. What is the minimum height of water necessary for resonance? (Speed of sound in air $= 340\, m/s$)

When the air column of a resonance tube is vibrated together with a tuning fork,$3$ beats are heard per second,either the temperature of the air column is $51^{\circ} C$ or $16^{\circ} C$. The frequency of the tuning fork is (in $Hz$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module