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  4. 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

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Q. 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

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Solution:

Let the tubes $A$ and $B$ have equal length $l$ Since, tube $A$ is open at both the ends, therefore, its fundamental frequency
$\upsilon_{A}=\frac{\upsilon}{2l} \ldots\left(i\right)$
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
$\frac{\upsilon_{A}}{\upsilon_{B}}=\frac{\upsilon 2l}{\upsilon 4l}=\frac{4}{2}=2 : 1$