The ratio of the frequencies of the fundamental harmonic produced by an open pipe to that of a closed pipe having the same length is

$A$ pipe open at both ends has a length of $1 \,m$. The air column in the pipe cannot resonate for which of the following frequencies (in $\,Hz$)? (Neglect end correction, speed of sound in air $= 340 \,m/s$)

$A$ student performed an experiment to measure the speed of sound in air using the resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,

$A$ pipe closed at one end produces a fundamental note of $412 \, Hz$. It is cut into two pieces of equal length. The fundamental notes produced by the two pieces are:

An open pipe is in resonance in its $2^{nd}$ harmonic with a tuning fork of frequency ${f_1}$. Now,it is closed at one end. If the frequency of the tuning fork is increased slowly from ${f_1}$,then again a resonance is obtained with a frequency ${f_2}$. If in this case the pipe vibrates in its $n^{th}$ harmonic,then:

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 ............... $Hz$.