The fundamental frequency of an open pipe is $100 \ Hz$. If the bottom end of the pipe is closed and $1/3$ rd of the pipe is filled with water,then the fundamental frequency of the pipe is: (in $Hz$)

$A$ closed organ pipe of length $L_1$ and an open organ pipe contain diatomic gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibilities of the gases are same in both pipes,which are vibrating in their first overtone with the same frequency. The length of the open organ pipe is (Neglect end correction).

$A$ flute,which we treat as a pipe open at both ends,is $34\, cm$ long. The fundamental frequency of the flute when all its holes are covered is .... $Hz$ [Take velocity of sound in air $= 340\, m/s$].

$A$ closed pipe and an open pipe have their first overtone equal in frequency. Then the lengths of these pipes are in the ratio

$A$ resonance tube closed at one end is of height $1.5 \ m$. $A$ tuning fork of frequency $340 \ Hz$ is vibrating above the tube. Water is poured in the tube gradually. The minimum height of water column for which resonance is obtained is . (Neglect end correction,speed of sound in air $= 340 \ m/s$) (in $cm$)

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.