$A$ pipe open at both ends and a pipe closed at one end have the same length. The ratio of the frequencies of their $P^{\text{th}}$ overtone is:

$Assertion :$ 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.

An organ pipe $P_1$ closed at one end has a vibrating air column in its first overtone,and another pipe $P_2$ open at both ends has a vibrating air column in the third overtone. Both are in resonance with a given tuning fork. The ratio of the length of pipe $P_1$ to that of $P_2$ is

$A$ pipe with $30 \ cm$ length is open at both ends. Which harmonic mode of the pipe resonates with a $1.65 \ kHz$ source? (Velocity of sound in air $= 330 \ m/s$)

$A$ pipe's lower end is immersed in water such that the length of the air column from the top open end has a length of $25 \, cm$. The speed of sound in air is $350 \, m/s$. The air column is found to resonate with a tuning fork of frequency $1750 \, Hz$. By what minimum distance should the pipe be raised in order to make the air column resonate again with the same tuning fork?

The frequency of the fourth overtone of a closed pipe is in unison with the fifth overtone of an open pipe. The ratio of the length of the closed pipe to that of the open pipe is