The frequency of the fourth overtone of a closed pipe is in unison with the fifth overtone of an open pipe. The ratio of the length of the closed pipe to that of the open pipe is

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

An organ pipe $40\,cm$ long is open at both ends. The speed of sound in air is $360\,ms^{-1}$. The frequency of the second harmonic is $...........\,Hz$.

$Assertion :$ The fundamental frequency of an open organ pipe increases as the temperature is increased.
$Reason :$ As the temperature increases,the velocity of sound increases more rapidly than the length of the pipe.

The fundamental frequency of an open pipe is $n$. If it is closed from one end, then the frequency of the $2^{nd}$ harmonic of the closed pipe is higher by $200 \,Hz$ than $n$. The value of $n$ is: (in $\,Hz$)

$A$ pipe $20 \; cm$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a $430 \; Hz$ source? Will the same source be in resonance with the pipe if both ends are open? (Speed of sound in air is $340 \; m/s$).