Give the equation for the normal modes of vibration for a closed pipe.

The first overtone frequency of a closed pipe of length $l_{1}$ is equal to the $2^{\text{nd}}$ harmonic frequency of an open pipe of length $l_{2}$. The ratio $\frac{l_{1}}{l_{2}}$ is:

At $23^{\circ} C$,a pipe open at both ends resonates at a frequency of $450 \,Hz$. At what frequency does the same pipe resonate on a hot day when the speed of sound is $4 \%$ higher than it would be at $23^{\circ} C$ (in $,Hz$)?

$A$ pipe open at both ends and a pipe closed at one end have the same length. The ratio of the frequencies of their $P^{\text{th}}$ overtone is:

$A$ 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 the $5$th overtone of an open organ pipe,the number of nodes $(N)$ and antinodes $(A)$ are: