$A$ pipe closed at one end has a length of $83 \ cm$. The number of possible natural oscillations of the air column whose frequencies lie below $1000 \ Hz$ are (velocity of sound in air $= 332 \ m/s$).

An open organ pipe is closed at one end such that the third overtone of the closed pipe is found to be higher in frequency by $200 \ Hz$ than the second overtone of the original open pipe. The fundamental frequency of the open pipe is (Neglect end correction). (in $Hz$)

The end correction for the vibrations of air column in a tube of circular cross-section will be more if the tube is

$A$ pipe open at both ends produces a fundamental frequency $n_1$. When the pipe is kept with $\frac{3}{4}$ of its length in water,it produces a note of fundamental frequency $n_2$. The ratio of $\frac{n_1}{n_2}$ is

An organ pipe of length $L$ is open at one end and closed at the other end. The wavelengths of the three lowest resonating frequencies that can be produced by this pipe are

$A$ pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to