Question

Tube $A$ has both ends open while tube $B$ has one end closed, otherwise they are identical. The ratio of fundamental frequency of tubes $A$ and $B$ is

• A. $1:2$
• B. $1:4$
• C. $2:1$
• D. $4:1$

Answer 1

Answer: (C)

Let the tubes $A$ and $B$ have equal length $l$ Since, tube $A$ is open at both the ends, therefore, its fundamental frequency
${\upsilon }_A=\frac{\upsilon }{2l}\dots \left(i\right)$
Since, tube $B$ is closed at one end, therefore, its fundamental frequency
${\upsilon }_B=\frac{\upsilon }{4l}$
From eqs. $\left(i\right)$ and $\left(ii\right)$, we get
$\frac{{\upsilon }_A}{{\upsilon }_B}=\frac{\upsilon 2l}{\upsilon 4l}=\frac{4}{2}=2:1$