First slide

Standing waves

Question

A closed organ pipe of length L and an open organ pipe contain gases of densities $ρ$ ₁ and $ρ$ 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 organ pipe is

Moderate

A

$L / 3$
B

$4 L / 3$
C

$\frac{4 L}{3} \sqrt{(\frac{ρ_{1}}{ρ_{2}})}$
D

$\frac{4 L}{3} \sqrt{(\frac{ρ_{2}}{ρ_{1}})}$

Solution

see fig
Let ,L' be the length of open pipe.
Given that $B_{1} = B_{2} = B (say)$
$Here L= \frac{3 λ_{1}}{4} and L^{'} = λ_{2} Now v_{1} = \sqrt{(\frac{B}{ρ_{1}})} and v_{2} = \sqrt{(\frac{B}{ρ_{2}})} \frac{v_{1}}{λ_{1}} = \frac{v_{2}}{λ_{2}} or \frac{3}{4 L} \sqrt{\frac{B}{ρ_{1}}} = \frac{1}{L^{'}} \sqrt{(\frac{B}{ρ_{2}})} L^{'} = \frac{4 L}{3} \sqrt{(\frac{ρ_{1}}{ρ_{2}})}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App