When an open pipe is closed from one end, the third overtone of the closed pipe is higher in frequency by $150 \text{ Hz}$ than the second overtone of the open pipe. The fundamental frequency of the open pipe will be (Neglect end correction). (in $\text{ Hz}$)

On closing an open organ pipe from one end, it is noticed that the frequency of the third harmonic is $50 \,Hz$ more than the fundamental frequency of vibration in the open organ pipe. The fundamental frequency of the open organ pipe is (in $\,Hz$)

The length of an open organ pipe is twice the length of a closed organ pipe. The fundamental frequency of the open pipe is $100 \ Hz$. The frequency of the third harmonic of the closed pipe is: (in $Hz$)

$A$ tuning fork of frequency $n$ is held near the open end of a tube which is closed at the other end,and the length is adjusted until resonance occurs. The first resonance occurs at length $L_1$ and the immediate next resonance occurs at length $L_2$. The speed of sound in air is

$A$ 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 closed and open organ pipes have the same length $L$. When they are vibrating simultaneously in their first overtone,they produce $4$ beats per second. The length of the open pipe is made half $(L/2)$ and that of the closed pipe is made two times $(2L)$ the original. Now,the number of beats produced if the two pipes are vibrating in their fundamental modes simultaneously is: