The number of possible natural oscillations of an air column in a pipe closed at one end of length $85 \, cm$ whose frequencies lie below $1250 \, Hz$ are (Velocity of sound $= 340 \, m s^{-1}$)

An open air pipe of length $80 \,cm$ has the second harmonic frequency equal to the fundamental frequency of a closed organ air pipe. The length of the closed pipe is (in $\,cm$)

$A$ 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 of length $L$ and an open organ pipe of length $L'$ contain gases of densities $\rho_{1}$ and $\rho_{2}$ respectively. The compressibility of the gases is equal in both pipes. Both pipes are vibrating in their first overtone with the same frequency. The length of the open pipe is $L' = \frac{x}{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}$,where $x$ is ......... . (Round off to the nearest integer)

$A$ tuning fork of frequency $n$ is held near the open end of a tube which is closed at the other end,and the length is adjusted until resonance occurs. The first resonance occurs at length $L_1$ and the immediate next resonance occurs at length $L_2$. The speed of sound in air is

$A$ pipe $20$ $cm$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of $1237.5$ $Hz$? (Speed of sound in air $= 330$ $m/s$).