If the velocity of sound in air is $350 \ m/s$,then the fundamental frequency of an open organ pipe of length $50 \ cm$ will be ............... $Hz$.

$A$ 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)

Give the equation for the normal modes of vibration for a closed pipe.

$A$ closed organ pipe and an open organ pipe have the same length $L$. When they are vibrating simultaneously in their first overtone,they produce $3$ beats per second. If the length of the open pipe is reduced to $\frac{1}{3}$ of its original length and the length of the closed pipe is increased to $3$ times its original length,calculate the number of beats produced per second. (Neglect end correction)

In a resonance tube open at one end, the end correction is $1.1$ cm. If the shortest length of resonating air column with a tuning fork is $18$ cm, the next resonating length will be (in $cm$)

$A$ cylindrical tube,open at both ends,has a fundamental frequency $f_0$ in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is