$A$ closed organ pipe has a fundamental frequency $n$. If its length is doubled and its radius is halved,its frequency nearly becomes

$A$ 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 organ pipe of length $L$ open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of $480 \, Hz$. What should be the length of a pipe closed at one end,so that it also vibrates in its first harmonic with the same tuning fork?

An organ pipe closed at one end has a fundamental frequency of $1500 \ Hz$. The maximum number of overtones generated by this pipe which a normal person can hear is:

$A$ closed pipe of length $10 \, cm$ has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe is ......... $cm$.

The end correction of a resonance column is $1 \, cm$. If the shortest length resonating with the tuning fork is $10 \, cm$,the next resonating length should be ..... $cm$.