In an experiment with a closed organ pipe of length $\ell$,it is filled with water by $\left(\frac{1}{5}\right)$ th of its volume. The frequency of the fundamental note will change by: (in $\%$)

In the fundamental mode,the time required for a sound wave to reach the closed end of an air-filled pipe is $t$ seconds. What is the frequency of vibration of the air column?

An open air pipe of length $80 \,cm$ has the second harmonic frequency equal to the fundamental frequency of a closed organ air pipe. The length of the closed pipe is (in $\,cm$)

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.

$A$ tuning fork of frequency $256\, Hz$ resonates with a closed organ pipe of length $25.4\, cm$. If the length of the pipe is increased by $2\, mm$,the number of beats per second will be:

$A$ tuning fork produces four beats per second with two open organ pipes having lengths $30 \ cm$ and $31 \ cm$. Find the frequency of the tuning fork in $Hz$.