The end correction of a resonance tube is $1 \ cm$. If the shortest length resonating with a tuning fork is $15 \ cm$,the next resonating length will be: (in $cm$)

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

An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of the length of the open pipe to that of the closed pipe is

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

$A$ wire of length $L$ and linear density $m$ is stretched between two rigid supports with tension $T$. It is observed that the wire resonates in the $P^{th}$ harmonic at a frequency of $320 \text{ Hz}$ and resonates again at the next higher frequency of $400 \text{ Hz}$ in two successive modes. The value of $P$ is

An air column,closed at one end and open at the other,resonates with a tuning fork when the smallest length of the column is $50\, cm$. The next larger length of the column resonating with the same tuning fork is .... $cm$.