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

What are closed pipe and open pipe?

$A$ metal rod of length $125 \ cm$ is clamped at its midpoint. If the speed of sound in the metal is $5000 \ ms^{-1}$, then the fundamental frequency of the longitudinal vibrations of the rod is (in $kHz$)

An open pipe of length $l$ is vibrating in the $3^{rd}$ overtone with a maximum amplitude $A$. The amplitude at a distance of $\frac{l}{16}$ from any open end is

$A$ source of frequency $340 \,Hz$ is kept above a vertical cylindrical tube closed at the lower end. The length of the tube is $120 \,cm$. Water is slowly poured in just enough to produce resonance. Then, the minimum height (velocity of sound $= 340 \,m/s$) of the water level in the tube for that resonance is (in $\,m$)

Explain the formation of stationary waves in a closed pipe and derive the equations for natural frequencies (normal modes).