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 ..... $m$.

$A$ tuning fork vibrating with a frequency of $512$ $Hz$ is kept close to the open end of a tube filled with water. The water level in the tube is gradually lowered. When the water level is $17$ $cm$ below the open end,maximum intensity of sound is heard. If the room temperature is $20^{\circ} C$,calculate:
$(a)$ Speed of sound in air at room temperature.
$(b)$ Speed of sound in air at $0^{\circ} C$.
$(c)$ If the water in the tube is replaced with mercury,will there be any difference in your observations?

$A$ pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of its length is in water. The fundamental frequency of the air column is now ..... $f$.

$A$ 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:

$A$ tuning fork is vibrating at $250\, {Hz}$. The length of the shortest closed organ pipe that will resonate with the tuning fork will be ..... ${cm}$.
(Take speed of sound in air as $340\, {ms}^{-1}$)

$A$ 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 $m$)