Two closed organ pipes of length $100 \,cm$ and $101 \,cm$ produce $16$ beats in $20 \,s$. When each pipe is sounded in its fundamental mode,calculate the velocity of sound in $m/s$.

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)

An open organ pipe of length $L$ vibrates in the second harmonic mode. The pressure vibration is maximum

$A$ closed organ pipe has length $L$. The air in it is vibrating in the third overtone with a maximum amplitude $a$. The amplitude at a distance $\frac{L}{7}$ from the closed end of the pipe is:

An organ pipe with both ends open has a length $L=25 \,cm$. An extra hole is created at position $\frac{L}{2}$. The lowest frequency of sound produced is (assume, speed of sound $=340 \,m/s$) (in $\,Hz$)

$A$ closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio