$A$ cylindrical tube open at both ends has a fundamental frequency of $390 \,Hz$ in air. If $\frac{1}{4}$th of the tube is immersed vertically in water, what is the fundamental frequency of the air column (in $\,Hz$)?

$n_{1}$ is the frequency of a pipe closed at one end and $n_{2}$ is the frequency of a pipe open at both ends. If both are joined end to end,find the fundamental frequency of the closed pipe so formed.

$A$ closed pipe of length $10 \, cm$ has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe is ......... $cm$.

$A$ closed organ pipe and an open organ pipe have the same length $L$. When they are vibrating simultaneously in their first overtone,they produce $3$ beats per second. If the length of the open pipe is reduced to $\frac{1}{3}$ of its original length and the length of the closed pipe is increased to $3$ times its original length,calculate the number of beats produced per second. (Neglect end correction)

The fundamental frequency of an air column in a pipe closed at one end is $100 \ Hz$. If the same pipe is open at both the ends,the frequencies produced in $Hz$ are

What should be the length of a closed pipe to produce resonance with a sound wave of wavelength $62 \,cm$,in fundamental mode (in $\,cm$)? [Neglect end correction]