$A$ 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 $= 330 \ m/s$)

If the end correction of an open pipe is $0.8 \,cm$, then the inner radius of that pipe is

The frequency of the third overtone of a pipe of length $L_c$,closed at one end,is the same as the frequency of the sixth overtone of a pipe of length $L_o$,open at both ends. Then the ratio $L_c : L_o$ is

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

$A$ $1 \; m$ long (both ends open) organ pipe is kept in a gas that has double the density of air at $STP$. Assuming the speed of sound in air at $STP$ is $300 \; m/s$,the frequency difference between the fundamental and second harmonic of this pipe is . . . . . . $Hz$.