The second overtone of an open organ pipe is equal to the first overtone of a closed organ pipe. If the length of the closed organ pipe is $15 \ cm$,the length of the open organ pipe is: (in $cm$)

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

$A$ pipe $30 \, cm$ long is open at both ends. Which harmonic mode of the pipe resonates with a $1.1 \, kHz$ source? (Speed of sound in air $= 330 \, m/s$)

An open pipe of length $33 \, cm$ resonates to a frequency of $1000 \, Hz$. The mode of vibration is: (velocity of sound $= 330 \, m/s$)

In the resonance experiment,two air columns (closed at one end) of $100 \ cm$ and $120 \ cm$ long,give $15$ beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is $:$ (in $m/s$)

An organ pipe $P_1$ closed at one end vibrating in its first overtone and another pipe $P_2$ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of $P_1$ and $P_2$ is