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 $= 333 \,m/s$)

$A$ student is performing the Resonance Column experiment. The diameter of the column tube is $4 \ cm$. The frequency of the tuning fork is $512 \ Hz$. The air temperature is $38^{\circ} C$,at which the speed of sound is $336 \ m/s$. The zero of the meter scale coincides with the top end of the resonance column. When the first resonance occurs,the reading of the water level in the column is: (in $cm$)

$A$ 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 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 ........ $m/s$.

In an organ pipe closed at one end,the sum of the frequencies of the first three overtones is $3930 \ Hz$. The frequency of the fundamental mode of the organ pipe is: (in $Hz$)

The fundamental frequency of a pipe is $100 \ Hz$ and the next two frequencies are $300 \ Hz$ and $500 \ Hz$. Then,the pipe is: