$A$ closed pipe is suddenly opened and changed to an open pipe of the same length. The fundamental frequency of the resulting open pipe is less than that of the $3^{rd}$ harmonic of the earlier closed pipe by $55 \,Hz$. Then, the value of the fundamental frequency of the closed pipe is: (in $\,Hz$)

$A$ tuning fork of frequency $340 \, Hz$ is sounded above an organ pipe of length $120 \, cm$. Water is now slowly poured in it. The minimum height of water column required for resonance is .... $cm$ (speed of sound in air $= 340 \, m/s$)

Two open organ pipes of lengths $50 \,cm$ and $51 \,cm$ are totally immersed in a medium. They are found to give $40$ beats in $10 \,s$ when each is sounding at its fundamental note. The speed of sound in this medium is (in $\,ms^{-1}$)

Two consecutive harmonics of an air column in a pipe closed at one end are of frequencies $150 \,Hz$ and $250 \,Hz$. The fundamental frequency of the air column is: (in $\,Hz$)

$A$ gas is filled in an organ pipe and it is sounded in its fundamental mode. Choose the correct statement$(s)$ : ($T$ = constant)

$A$ closed organ pipe and an open organ pipe are filled with two different gases having the same bulk modulus but different densities $\rho_1$ and $\rho_2$ respectively. The frequency of the $9^{\text{th}}$ harmonic of the closed pipe is identical to the $4^{\text{th}}$ harmonic of the open pipe. If the length of the closed pipe is $10 \ cm$ and the density ratio of the gases is $\rho_1 : \rho_2 = 1 : 16$,then the length of the open pipe is: