$A$ pipe closed at one end produces a fundamental note of $412 \, Hz$. It is cut into two pieces of equal length. The fundamental notes produced by the two pieces are:

$A$ 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 $\,Hz$)?

$A$ closed pipe and an open pipe have their first overtone equal in frequency. Then the lengths of these pipes are in the ratio

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1:$ In the resonance tube experiment,if the tuning fork is replaced by another identical tuning fork but with its arms filed,the length of the air column should be increased to obtain resonance again.
Statement $2:$ On filing the arms,the frequency of a tuning fork increases.

$A$ closed organ pipe of length $L_c$ and an open organ pipe of length $L_o$ contain different gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibility of the gases is the same in both the pipes. The gases are vibrating in their first overtone with the same frequency. What is the length of the open organ pipe?

If the speed of sound in air is $330 \, m/s$,find the number of tones (harmonics) present in an open organ pipe of length $1 \, m$ whose frequency is $\leq 1000 \, Hz$.