A closed organ pipe of length L and an open organ pipe contain ga… - Vidyadip

MCQ

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 gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $\frac{ x }{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}$ where $x$ is ......... . (Round off to the Nearest Integer)

✓
$4$
B
$6$
C
$2$
D
$1$

✓

Answer

Correct option: A.

$4$

a
$f_{c}=f_{0}$

$\frac{3 V_{C}}{4 L}=\frac{2 V_{0}}{2 L^{\prime}}$

$\frac{3 V_{C}}{4 L}=\frac{V_{0}}{L^{\prime}}$

$L ^{\prime}=\frac{4 L }{3} \frac{ V _{0}}{ V _{ C }}=\frac{4 L }{3} \sqrt{\frac{ B \cdot \rho_{1}}{\rho_{2} \cdot B }}( B$ is bulk modulus)

$=\frac{4 L }{3} \sqrt{\frac{\rho_{1}}{\rho_{2}}}$

$x =4$

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