For a certain organ pipe,three successive resonance frequencies are observed at $425 \, Hz$,$595 \, Hz$,and $765 \, Hz$ respectively. If the speed of sound in air is $340 \, m/s$,then the length of the pipe is ..... $m$.

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:

Two similar open organ pipes of length $50 \, cm$ and $50.5 \, cm$ produce $3$ beats per second when sounded together. The velocity of sound in air is ........ $m/s$.

$A$ closed pipe is suddenly opened and changed to an open pipe of the same length. The fundamental frequency of the resulting open pipe is less than that of the $3^{rd}$ harmonic of the earlier closed pipe by $55 \,Hz$. Then, the value of the fundamental frequency of the closed pipe is: (in $\,Hz$)

In a resonance tube experiment,two consecutive resonances are observed when the lengths of the air columns are $16 \ cm$ and $49 \ cm$. If the frequency of the tuning fork used is $500 \ Hz$,the velocity of sound in air is $... \ ms^{-1}$.

If the temperature increases,then what happens to the frequency of the sound produced by the organ pipe?