In a pipe closed at one end,an air column is vibrating in its second overtone. The column has

$A$ resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of sound in air. $A$ tuning fork of frequency $512\,Hz$ produces the first resonance when the tube is filled with water to a mark $11\,cm$ below a reference mark,near the open end of the tube. The experiment is repeated with another fork of frequency $256\,Hz$,which produces the first resonance when water reaches a mark $27\,cm$ below the reference mark. The velocity of sound in air,obtained in the experiment,is close to .... $ms^{-1}$

In a resonance tube experiment,when the tube is filled with water up to a height of $17.0 \, cm$ from the bottom,it resonates with a given tuning fork. When the water level is raised,the next resonance with the same tuning fork occurs at a height of $24.5 \, cm$. If the velocity of sound in air is $330 \, m/s$,the tuning fork frequency is $...... \, Hz$.

The fundamental frequency of a closed pipe is $400 \text{ Hz}$. If $\left(\frac{1}{3}\right)^{rd}$ length of the pipe is filled with water, the frequency of the $2^{\text{nd}}$ harmonic of the pipe will be (Neglect end correction). (in $\text{ Hz}$)

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

$A$ closed organ pipe of radius $r_1$ and an open organ pipe of radius $r_2$ having the same length $L$ resonate when excited with a given tuning fork. The closed organ pipe resonates in its fundamental mode,whereas the open organ pipe resonates in its first overtone. Then: