When an air column in a pipe open at both ends vibrates such that four antinodes and three nodes are formed,then the corresponding mode of vibration is

In an experiment to measure the speed of sound by a resonating air column,a tuning fork of frequency $500 \text{ Hz}$ is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length $50.7 \text{ cm}$ and $83.9 \text{ cm}$. Which of the following statements is (are) true?
$(A)$ The speed of sound determined from this experiment is $332 \text{ m s}^{-1}$
$(B)$ The end correction in this experiment is $0.9 \text{ cm}$
$(C)$ The wavelength of the sound wave is $66.4 \text{ cm}$
$(D)$ The resonance at $50.7 \text{ cm}$ corresponds to the fundamental harmonic

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

An organ pipe of length $L$ is open at one end and closed at the other end. The wavelengths of the three lowest resonating frequencies that can be produced by this pipe are

An open pipe of length $l$ is vibrating in the $3^{rd}$ overtone with a maximum amplitude $A$. The amplitude at a distance of $\frac{l}{16}$ from any open end is

$A$ pipe open at both ends and a pipe closed at one end have the same length. The ratio of the frequencies of the air columns in their $p^{\text{th}}$ overtone respectively is