An organ pipe $P_1$ closed at one end has a vibrating air column in its first overtone,and another pipe $P_2$ open at both ends has a vibrating air column in the third overtone. Both are in resonance with a given tuning fork. The ratio of the length of pipe $P_1$ to that of $P_2$ is

Two open organ pipes of fundamental frequencies $n_{1}$ and $n_{2}$ are joined in series. The fundamental frequency of the new pipe so obtained will be

In an open organ pipe,$v_3$ and $v_6$ are the $3^{\text{rd}}$ and $6^{\text{th}}$ harmonic frequencies,respectively. If $v_6 - v_3 = 2200 \text{ Hz}$,then the length of the pipe is . . . . . . mm. (Take the velocity of sound in air as $330 \text{ m/s}$.)

An organ pipe $P_1$,closed at one end and containing a gas of density $\rho_1$ is vibrating in its first harmonic. Another organ pipe $P_2$,open at both ends and containing a gas of density $\rho_2$ is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes,the ratio of the lengths of $P_1$ and $P_2$ is (assume the given gases to be monoatomic)

$A$ string of length $3 \ m$ and linear mass density $0.0025 \ kg/m$ is fixed at both ends. One of its resonance frequencies is $252 \ Hz$. The next higher resonance frequency is $336 \ Hz$. Then the fundamental frequency will be ..... $Hz$.

If a pipe gives notes of frequencies $375 \ Hz$,$625 \ Hz$,and $875 \ Hz$,what is the fundamental frequency of the pipe and its type?