$A$ cylindrical tube,open at both ends,has a fundamental frequency $f_0$ in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is

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

If the end correction of an open pipe is $0.8 \,cm$, then the inner radius of that pipe is

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

$A$ pipe closed at one end produces a fundamental note of $412 \, Hz$. It is cut into two pieces of equal length. The fundamental notes produced by the two pieces are:

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 $\text{ Hz}$)