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 $...........\,Hz$.

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

If the fundamental frequency of a closed pipe is $50\,Hz$,then the frequency of the $2^{nd}$ overtone is .... $Hz$.

$A$ closed organ pipe and an open organ pipe have the same length $L$. When they are vibrating simultaneously in their first overtone,they produce $3$ beats per second. If the length of the open pipe is reduced to $\frac{1}{3}$ of its original length and the length of the closed pipe is increased to $3$ times its original length,calculate the number of beats produced per second. (Neglect end correction)

$A$ pipe $P_{C}$ closed at one end and a pipe $P_{O}$ open at both ends are vibrating in their second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe $P_{C}$ to $P_{O}$ is (Neglect end correction):

An air column in a tube of length $L = 50 \ cm$, closed at one end, is vibrating in its fifth harmonic. The phase difference between a particle at the open end and a particle at $42 \ cm$ from the open end is: (in $^{\circ}$)