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 $= 340 \, m s^{-1}$)

$Assertion :$ 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.

$A$ student is performing the Resonance Column experiment. The diameter of the column tube is $4 \ cm$. The frequency of the tuning fork is $512 \ Hz$. The air temperature is $38^{\circ} C$,at which the speed of sound is $336 \ m/s$. The zero of the meter scale coincides with the top end of the resonance column. When the first resonance occurs,the reading of the water level in the column is: (in $cm$)

At a temperature of $27^{\circ} C$, two identical organ pipes produce notes of frequency $140 \,Hz$. If the temperature of one pipe is raised to $57.75^{\circ} C$, then the number of beats produced per second is

$A$ 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?

$A$ taut string fixed at both ends vibrates in its $n^{th}$ overtone. The distance between adjacent Node and Antinode is found to be $d$. If the length of the string is $L$,then: