In the $5$th overtone of an open organ pipe,the number of nodes $(N)$ and antinodes $(A)$ are:

$A$ string fixed at both ends is in resonance in its $2^{nd}$ harmonic with a tuning fork of frequency $f_1$. Now,one end becomes free. If the frequency of the tuning fork is increased slowly from $f_1$,then again a resonance is obtained when the frequency is $f_2$. If in this case the string vibrates in the $n^{th}$ harmonic,then:

$Assertion :$ The fundamental frequency of an open organ pipe increases as the temperature is increased.
$Reason :$ As the temperature increases,the velocity of sound increases more rapidly than the length of the pipe.

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 ..... $m$.

The number of possible natural oscillations of an air column in a pipe closed at one end of length $85 \, cm$ whose frequencies lie below $1250 \, Hz$ are (Velocity of sound $= 340 \, m s^{-1}$)

In an open organ pipe, $v_3$ and $v_6$ are the $3^{\text{rd}}$ and $6^{\text{th}}$ harmonic frequencies, respectively. If $v_6 - v_3 = 2200 \text{ Hz}$, then the length of the pipe is . . . . . . mm. (Take the velocity of sound in air as $330 \text{ m/s}$.)