$A$ cylindrical tube open at both ends has a fundamental frequency $f$ in air. When the tube is dipped vertically in water so that one-third part of the tube is in water,the fundamental frequency of the air column becomes (neglect end correction).

Sound waves of frequency $600 \,Hz$ fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration is (speed of sound $= 300 \,ms^{-1}$)

$A$ 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 .... $m/s$.

The fundamental frequencies of vibrations of an air column in a pipe open at both ends and in a pipe closed at one end are $n_1$ and $n_2$ respectively. If both pipes have the same length $L$,then:

$A$ closed pipe of length $10 \, cm$ has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe is ......... $cm$.

$A$ closed pipe is in resonance with a tuning fork at $27^{\circ} C$ when its length is $20 \,cm$. If the pipe is to be in resonance with the same tuning fork at $7^{\circ} C$, then the change in the length of the pipe required is nearly: (in $\,mm$)