An open organ pipe of length l is sounded tog | vedclass

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

Question

(B) For an open organ pipe of length $L$,the fundamental frequency is given by $f = \frac{V}{2L}$.For the first pipe of length $l$,the fundamental fre

Vedclass · Accepted Answer

$\frac{V l_1}{2 l^2}$

Vedclass · Answer

(B) For an open organ pipe of length $L$,the fundamental frequency is given by $f = \frac{V}{2L}$.For the first pipe of length $l$,the fundamental frequency is $f_1 = \frac{V}{2l}$.For the second pipe of length $(l+l_1)$,the fundamental frequency is $f_2 = \frac{V}{2(l+l_1)}$.The beat frequency $f_b$ is the difference between the two frequencies: $f_b = f_1 - f_2 = \frac{V}{2l} - \frac{V}{2(l+l_1)}$.Simplifying the expression: $f_b = \frac{V}{2} \left[ \frac{(l+l_1) - l}{l(l+l_1)} \right] = \frac{V l_1}{2l(l+l_1)}$.Given the condition $l_1 \ll l$,we can approximate $(l+l_1) \approx l$ in the denominator.Therefore,$f_b \approx \frac{V l_1}{2l^2}$.

An open organ pipe of length $l$ is sounded together with another open organ pipe of length $(l+l_1)$ in their fundamental modes. Speed of sound in air is $V$. The beat frequency heard will be $(l_1 \ll l)$

Similar Questions

$A$ tuning fork of frequency '$n$' is held near the open end of a tube which is dipped in water and length of the tube is adjusted until resonance occurs. If the two shortest lengths that produce resonance are $l_1$ and $l_2$, the speed of sound in air is (neglect end correction)

$A$ closed organ pipe of radius $r_1$ and an open organ pipe of radius $r_2$ having the same length $L$ resonate when excited with a given tuning fork. The closed organ pipe resonates in its fundamental mode,whereas the open organ pipe resonates in its first overtone. Then:

$A$ closed organ pipe of length $l$ is sounded together with another closed organ pipe of length $l + x$ $(x << l)$,both in their fundamental mode. If $v$ is the speed of sound,the beat frequency heard is:

For a certain organ pipe,three successive resonance frequencies are observed at $425 \, Hz$,$595 \, Hz$,and $765 \, Hz$ respectively. If the speed of sound in air is $340 \, m/s$,then the length of the pipe is ..... $m$.

$A$ 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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module