$A$ whistle whose air column is open at both ends has a fundamental frequency of $5100 \ Hz$. If the speed of sound in air is $340 \ ms^{-1}$,the length of the whistle,in $cm$,is

When an air column in a pipe open at both ends vibrates such that four antinodes and three nodes are formed,then the corresponding mode of vibration is

The ratio of the frequencies of the first overtone produced by an open pipe to that of a closed pipe having the same length is

$A$ metre-long tube open at one end,with a movable piston at the other end,shows resonance with a fixed frequency source (a tuning fork of frequency $340\; Hz$) when the tube length is $25.5\; cm$ or $79.3\; cm$. Estimate the speed of sound (in $m/s$) in air at the temperature of the experiment. The edge effects may be neglected.

$Assertion :$ 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.

$A$ source of frequency $340 \,Hz$ is kept above a vertical cylindrical tube closed at the lower end. The length of the tube is $120 \,cm$. Water is slowly poured in just enough to produce resonance. Then, the minimum height (velocity of sound $= 340 \,m/s$) of the water level in the tube for that resonance is (in $\,m$)