$A$ cylindrical tube,open at both ends,has a fundamental frequency $f_0$ in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is

$A$ $1 \; m$ long (both ends open) organ pipe is kept in a gas that has double the density of air at $STP$. Assuming the speed of sound in air at $STP$ is $300 \; m/s$,the frequency difference between the fundamental and second harmonic of this pipe is . . . . . . $Hz$.

In a closed organ pipe, the number of nodes formed in the fifth and ninth harmonics are respectively:

$A$ string of length $3 \ m$ and linear mass density $0.0025 \ kg/m$ is fixed at both ends. One of its resonance frequencies is $252 \ Hz$. The next higher resonance frequency is $336 \ Hz$. Then the fundamental frequency will be ..... $Hz$.

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 $= 340 \, m s^{-1}$)

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $5 / x$. The value of $x$ is . . . . . . .