In the resonance experiment,two air columns (closed at one end) of $100 \ cm$ and $120 \ cm$ long,give $15$ beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is $:$ (in $m/s$)

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

$A$ pipe with $30 \ cm$ length is open at both ends. Which harmonic mode of the pipe resonates with a $1.65 \ kHz$ source? (Velocity of sound in air $= 330 \ m/s$)

$A$ pipe $17 \, cm$ long is closed at one end. Which harmonic mode of the pipe resonates with a $1.5 \, kHz$ source? (Speed of sound in air $= 340 \, m \, s^{-1}$)

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.

In fundamental mode,the time required for the sound wave to reach up to the closed end of a pipe filled with air is $t$ seconds. The frequency of vibration of the air column is