An open and a closed organ pipe are of same length. The ratio of the frequency of the $n^{th}$ mode of vibration of the two pipes is

$A$ closed organ pipe and an open organ pipe of the same length produce $2$ beats per second when they are set into vibrations together in their fundamental mode. The length of the open pipe is now halved and that of the closed pipe is doubled. The number of beats produced per second will be:

$Assertion :$ 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.

The pitch of an organ pipe is highest when the pipe is filled with

$A$ pipe open at both ends has a fundamental frequency '$f$' in air. The pipe is dipped in water, so that $\frac{2}{3}$ of its length is in water. Now, the fundamental frequency of the air column is:

Two closed organ pipes,when sounded simultaneously,give $4$ beats per second. If the longer pipe has a length of $1 \ m$,then the length of the shorter pipe will be,... $cm$ $(v = 300 \ m/s)$.