While measuring the speed of sound by performing a resonance column experiment,a student gets the first resonance condition at a column length of $18\,cm$ during winter. Repeating the same experiment during summer,she measures the column length to be $x\,cm$ for the second resonance. Then

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1:$ In the resonance tube experiment,if the tuning fork is replaced by another identical tuning fork but with its arms filed,the length of the air column should be increased to obtain resonance again.
Statement $2:$ On filing the arms,the frequency of a tuning fork increases.

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

$A$ tube closed at one end and containing air is excited. It produces the fundamental note of frequency $512 \ Hz$. If the same tube is open at both ends,the fundamental frequency that can be produced is .... $Hz$.

$A$ resonance tube completely filled with water has a small hole at the bottom. Length of the tube is $0.8 \ m$. $A$ vibrating tuning fork of frequency $500 \ Hz$ is held near the open end of the tube. Water is slowly removed from the bottom. The maximum number of resonances heard will be (Neglect end correction. Speed of sound in air $= 340 \ m/s$).

An organ pipe $P_1$ closed at one end vibrating in its first overtone and another pipe $P_2$ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of $P_1$ and $P_2$ is