An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

$A$ closed organ pipe of length $L$ and an open organ pipe contain gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibility of the gases is equal in both the pipes. If the frequencies of their first overtones are the same,then the length of the open organ pipe is:

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 $m$)

An air column is of length $17 \ cm$. The ratio of frequencies of the $5^{\text{th}}$ overtone for an air column closed at one end to that open at both ends is (velocity of sound in air $= 340 \ ms^{-1}$).

$A$ pipe $17 \, cm$ long is closed at one end. Which harmonic mode of the pipe resonates with a $1.5 \, kHz$ source? (Speed of sound in air $= 340 \, m \, s^{-1}$)

In an organ pipe whose one end is at $x = 0$,the pressure is expressed by $p = p_0 \cos \frac{3\pi x}{2} \sin 300\pi t$,where $x$ is in meters and $t$ is in seconds. The organ pipe can be: