$A$ pipe open at both ends and a pipe closed at one end have the same length and both are vibrating in their fundamental mode. If the air column vibrating in the open pipe has a resonance frequency $n_1$ and the air column vibrating in the closed pipe has a resonance frequency $n_2$,then:

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

An open pipe is suddenly closed at one end with the result that the frequency of the third harmonic of the closed pipe is found to be higher by $100 \ Hz$ than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is .... $Hz$.

In an experiment to measure the speed of sound by a resonating air column,a tuning fork of frequency $500 \text{ Hz}$ is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length $50.7 \text{ cm}$ and $83.9 \text{ cm}$. Which of the following statements is (are) true?
$(A)$ The speed of sound determined from this experiment is $332 \text{ m s}^{-1}$
$(B)$ The end correction in this experiment is $0.9 \text{ cm}$
$(C)$ The wavelength of the sound wave is $66.4 \text{ cm}$
$(D)$ The resonance at $50.7 \text{ cm}$ corresponds to the fundamental harmonic

In a resonance tube experiment,the first and second resonance are heard when the water level is $24.1 \ cm$ and $74.1 \ cm$ respectively,below the open end of the tube. The inner diameter of the tube is (in $cm$)

$A$ pipe's lower end is immersed in water such that the length of the air column from the top open end has a length of $25 \, cm$. The speed of sound in air is $350 \, m/s$. The air column is found to resonate with a tuning fork of frequency $1750 \, Hz$. By what minimum distance should the pipe be raised in order to make the air column resonate again with the same tuning fork?