$A$ pipe of $30 \text{ cm}$ long and open at both ends produces harmonics. Which harmonic mode of the pipe resonates with a $1.1 \text{ kHz}$ source? (Given: speed of sound in air $v = 330 \text{ ms}^{-1}$)

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

The vibrations of four air columns under identical conditions are represented in the figure below. The ratio of frequencies $n_p: n_q: n_r: n_s$ will be

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube,the first resonance is observed when the air column has a length of $20.0 \,cm$ for a tuning fork of frequency $400 \,Hz$. The velocity of sound at room temperature is $336 \,ms^{-1}$. The third resonance is observed when the air column has a length of ......... $cm$.

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

$A$ taut string fixed at both ends vibrates in its $n^{th}$ overtone. The distance between adjacent Node and Antinode is found to be $d$. If the length of the string is $L$,then: