$A$ tuning fork of frequency '$n$' is held near the open end of a tube which is dipped in water and length of the tube is adjusted until resonance occurs. If the two shortest lengths that produce resonance are $l_1$ and $l_2$, the speed of sound in air is (neglect end correction)

$A$ pipe open at both ends and a pipe closed at one end have the same length and both are vibrating in their fundamental mode. If the air column vibrating in the open pipe has a resonance frequency $n_1$ and the air column vibrating in the closed pipe has a resonance frequency $n_2$,then:

An organ pipe closed at one end has a fundamental frequency of $1500 \ Hz$. The maximum number of overtones generated by this pipe which a normal person can hear 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.

$A$ pipe open at both ends of length $1.5 \,m$ is dipped in water such that the second overtone of the vibrating air column resonates with a tuning fork of frequency $330 \,Hz$. If the speed of sound in air is $330 \,m/s$, then the length of the pipe immersed in water is (Neglect end correction). (in $\,m$)

The vibrations of four air columns are shown below. The ratio of frequencies is