$A$ pipe $P_{C}$ closed at one end and a pipe $P_{O}$ open at both ends are vibrating in their second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe $P_{C}$ to $P_{O}$ is (Neglect end correction):

Consider the following statements about stationary waves:
$A$. The distance between two adjacent nodes or antinodes is equal to $\frac{\lambda}{2}$ $(\lambda = \text{wavelength of the wave})$.
$B$. $A$ pressure node is always formed at the open end of the open organ pipe.
Choose the correct option from the following:

If the fundamental frequency of a closed pipe is $50\,Hz$,then the frequency of the $2^{nd}$ overtone is .... $Hz$.

In a pipe closed at one end,an air column is vibrating in the fourth overtone. How many nodes and antinodes does the vibrating air column have?

If the speed of sound in air is $330 \, m/s$,find the number of tones (harmonics) present in an open organ pipe of length $1 \, m$ whose frequency is $\leq 1000 \, Hz$.

$A$ pipe open at both ends of length $1.5 \ m$ is dipped in water at one end such that the $2^{\text{nd}}$ overtone of the vibrating air column is resonating with a tuning fork of frequency $330 \ Hz$. The length of the pipe immersed in water is (Speed of sound in air $= 330 \ m/s$) (Neglect end correction). (in $m$)