The first overtone frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. Further,the $n^{th}$ harmonic of the closed organ pipe is also equal to the $m^{th}$ harmonic of the open pipe,where $n$ and $m$ are:

$A$ tuning fork of frequency $340\, Hz$ is vibrated just above a tube of $120\, cm$ height. Water is poured slowly into the tube. What is the minimum height of water necessary for resonance? (Speed of sound in air $= 340\, m/s$)

$A$ pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to

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.

When an open pipe is closed from one end, the third overtone of the closed pipe is higher in frequency by $150 \text{ Hz}$ than the second overtone of the open pipe. The fundamental frequency of the open pipe will be (Neglect end correction). (in $\text{ Hz}$)

What is the base frequency if a pipe gives notes of frequencies $425 \text{ Hz}, 255 \text{ Hz},$ and $595 \text{ Hz}$? Also,decide whether the pipe is closed at one end or open at both ends.