Two open organ pipes of length $50 \, cm$ and $50.5 \, cm$ produce $3$ beats per second. The velocity of sound is ..... $m/s$.

$A$ 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)

Two open organ pipes of length $60 \,cm$ and $90 \,cm$ resonate at $6^{\text{th}}$ and $5^{\text{th}}$ harmonics respectively. The difference of frequencies for the given modes is . . . . . $Hz$.
(Velocity of sound in air $= 333 \,m/s$)

The vibrations of four air columns under identical conditions are represented in the figure below. The ratio of frequencies $n_p: n_q: n_r: n_s$ will be

Two similar open organ pipes of length $50 \, cm$ and $50.5 \, cm$ produce $3$ beats per second when sounded together. The velocity of sound in air is ........ $m/s$.

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of the open pipe is $60 \,cm$, the length of the closed pipe will be: (in $\,cm$)