The length of an open organ pipe is twice the length of another closed organ pipe. The fundamental frequency of the open pipe is $100 \ Hz$. The frequency of the third harmonic of the closed pipe is ..... $Hz$.

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

The first overtone of the vibrating air column of a closed pipe has the same frequency as the second overtone of an open pipe $1.5 \ m$ long. The length of the closed pipe is (in $m$)

In the $5$th overtone of an open organ pipe,the number of nodes $(N)$ and antinodes $(A)$ are:

An organ pipe filled with a gas at $27^{\circ}C$ resonates at $400\,Hz$ in its fundamental mode. If it is filled with the same gas at $90^{\circ}C$,the resonance frequency at the same mode will be $...........\,Hz$.

$A$ 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