$A$ closed organ pipe of radius $r_1$ and an open organ pipe of radius $r_2$ having the same length $L$ resonate when excited with a given tuning fork. The closed organ pipe resonates in its fundamental mode,whereas the open organ pipe resonates in its first overtone. Then:

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

The $3^{\text{rd}}$ overtone of a closed organ pipe is in unison with the $3^{\text{rd}}$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

$A$ 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 $= 332 \ m/s$).

$A$ tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27\,^{\circ}C$,two successive resonances are produced at $20\,cm$ and $73\,cm$ of column length. If the frequency of the tuning fork is $320\,Hz$,the velocity of sound in air at $27\,^{\circ}C$ is .... $m/s$.

Two open organ pipes of fundamental frequencies $n_{1}$ and $n_{2}$ are joined in series. The fundamental frequency of the new pipe is