$A$ student is performing the experiment of Resonance Column. The diameter of the column tube is $4 \ cm$. The frequency of the tuning fork is $512 \ Hz$. The air temperature is $38^{\circ}C$ in which the speed of sound is $336 \ m/s$. The zero of the meter scale coincides with the top end of the Resonance column tube. When the first resonance occurs,the reading of the water level in the column is ..... $cm$.

One insulated conductor from a household extension cord has a mass per unit length of $\mu$. $A$ section of this conductor is held under tension between two clamps. $A$ subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the length of the cord. When the cord carries an $AC$ current of $i$ at a frequency of $f$,it vibrates in resonance in its simplest standing-wave vibration state. Determine the relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.

An organ pipe closed at one end produces a fundamental note of frequency '$\nu$'. The pipe is cut into two pipes of equal length. The fundamental frequencies produced in the two pipes are

The fundamental frequency of a pipe is $100 \ Hz$ and the next two frequencies are $300 \ Hz$ and $500 \ Hz$. Then:

Discuss stationary waves in pipes and explain the types of pipes.

$A$ tuning fork of frequency $340 \ Hz$ is vibrated just above a tube of $120 \ cm$ height. Water is slowly poured in the tube. What is the minimum height of water necessary for resonance (in $cm$)?