The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is $20 \, cm$,the length of the open organ pipe is ........ $cm$.

An organ pipe open at one end is vibrating in its first overtone and is in resonance with another pipe open at both ends vibrating in its third harmonic. The ratio of the length of the two pipes is:

$A$ cylindrical tube,open at both ends,has a fundamental frequency $f_0$ in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is

In a closed organ pipe,the frequency of the fundamental note is $50 \ Hz$. Which of the following frequencies will not be emitted by it?

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

Consider the following statements about stationary waves:
$A$. The distance between two adjacent nodes or antinodes is equal to $\frac{\lambda}{2}$ $(\lambda = \text{wavelength of the wave})$.
$B$. $A$ pressure node is always formed at the open end of the open organ pipe.
Choose the correct option from the following: