What should be the length of a closed pipe to produce resonance with a sound wave of wavelength $62 \,cm$,in fundamental mode (in $\,cm$)? [Neglect end correction]

An open organ pipe of length $l$ is sounded together with another organ pipe of length $l + x$ in their fundamental tones $(x << l)$. The beat frequency heard will be (speed of sound is $v$):

In an experiment with a closed organ pipe of length $\ell$,it is filled with water by $\left(\frac{1}{5}\right)$ th of its volume. The frequency of the fundamental note will change by: (in $\%$)

Two pipes are each $50\,cm$ in length. One of them is closed at one end while the other is open at both ends. The speed of sound in air is $340\,ms^{-1}.$ The frequency at which both the pipes can resonate is

An organ pipe $P_1$,closed at one end,is vibrating in its first harmonic. Another pipe $P_2$,open at both ends,is vibrating in its third harmonic. Both are in resonance with a given tuning fork. The ratio of the lengths of $P_1$ and $P_2$ is:

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 $m/s$.