$A$ tuning fork vibrates with frequency $256\, Hz$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe in $cm$? (Speed of sound in air is $340\, m/s$)

$A$ closed organ pipe of length $L$ and an open organ pipe of length $L'$ contain gases of densities $\rho_{1}$ and $\rho_{2}$ respectively. The compressibility of the gases is equal in both pipes. Both pipes are vibrating in their first overtone with the same frequency. The length of the open pipe is $L' = \frac{x}{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}$,where $x$ is ......... . (Round off to the nearest integer)

The end correction of a resonance column is $1 \, cm$. If the shortest length resonating with the tuning fork is $10 \, cm$,the next resonating length should be ..... $cm$.

An organ pipe closed at one end has a fundamental frequency of $1500 \ Hz$. The maximum number of overtones generated by this pipe which a normal person can hear is:

For a certain organ pipe,three successive resonance frequencies are observed at $425 \, Hz$,$595 \, Hz$,and $765 \, Hz$ respectively. If the speed of sound in air is $340 \, m/s$,then the length of the pipe is ..... $m$.

$A$ tuning fork of frequency $256\, Hz$ resonates with a closed organ pipe of length $25.4\, cm$. If the length of the pipe is increased by $2\, mm$,the number of beats per second will be: