The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is $20 \, cm$,the length of the open organ pipe is ........ $cm$.

$A$ string is stretched between fixed points separated by $75.0\, cm$. It is observed to have resonant frequencies of $420\, Hz$ and $315\, Hz$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is .... $Hz$.

$A$ cylindrical tube $(L = 120\,cm)$ is resonant with a tuning fork of frequency $330\,Hz$. If it is being filled with water,what is the minimum length of the water column required to achieve resonance? (Speed of sound in air $V_{air} = 330\,m/s$)

In an experiment with a closed organ pipe of length $\ell$,it is filled with water by $\left(\frac{1}{5}\right)$ th of its volume. The frequency of the fundamental note will change by: (in $\%$)

$A$ closed pipe is suddenly opened and changed to an open pipe of the same length. The fundamental frequency of the resulting open pipe is less than that of the $3^{rd}$ harmonic of the earlier closed pipe by $55 \,Hz$. Then, the value of the fundamental frequency of the closed pipe is: (in $\,Hz$)

$A$ pipe closed at one end has a length of $83 \ cm$. The number of possible natural oscillations of the air column whose frequencies lie below $1000 \ Hz$ are (velocity of sound in air $= 332 \ m/s$).