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 $\text{ Hz}$)

An air column in a pipe,which is closed at one end,will be in resonance with a vibrating tuning fork of frequency $264 \, Hz$ if the length of the column in $cm$ is (velocity of sound $= 330 \, m/s$)

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:

$A$ pipe open at both ends of length $1.5 \,m$ is dipped in water such that the second overtone of the vibrating air column resonates with a tuning fork of frequency $330 \,Hz$. If the speed of sound in air is $330 \,m/s$, then the length of the pipe immersed in water is (Neglect end correction). (in $\,m$)

An organ pipe $P_1$ closed at one end vibrating in its first overtone and another pipe $P_2$ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of $P_1$ and $P_2$ is

In the fundamental mode,the time taken by the wave to reach the closed end of an air-filled pipe is $0.01 \ s$. The fundamental frequency is (in $Hz$)