The fundamental frequency of an air column in a pipe closed at one end is $100 \ Hz$. If the same pipe is open at both the ends,the frequencies produced in $Hz$ are

In an organ pipe closed at one end,the sum of the frequencies of the first three overtones is $3930 \ Hz$. The frequency of the fundamental mode of the organ pipe is: (in $Hz$)

Two open organ pipes of length $50 \, cm$ and $50.5 \, cm$ produce $3$ beats per second. The velocity of sound is ..... $m/s$.

The frequency of the third overtone of a pipe of length $L_c$,closed at one end,is the same as the frequency of the sixth overtone of a pipe of length $L_o$,open at both ends. Then the ratio $L_c : L_o$ is

An open and a closed organ pipe are of same length. The ratio of the frequency of the $n^{th}$ mode of vibration of the two pipes 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