When an air column in a pipe open at both ends vibrates such that four antinodes and three nodes are formed,then the corresponding mode of vibration is

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube,the first resonance is observed when the air column has a length of $20.0 \,cm$ for a tuning fork of frequency $400 \,Hz$. The velocity of sound at room temperature is $336 \,ms^{-1}$. The third resonance is observed when the air column has a length of ......... $cm$.

The length of a closed and an open pipe is the same. The ratio of the frequency of the $n^{\text{th}}$ overtone for the closed pipe to that of the open pipe is (Neglect end correction).

$A$ closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio:

An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

Two open organ pipes of lengths $50 \,cm$ and $51 \,cm$ are totally immersed in a medium. They are found to give $40$ beats in $10 \,s$ when each is sounding at its fundamental note. The speed of sound in this medium is (in $\,ms^{-1}$)