The fundamental frequency of an open pipe of length $0.5 \ m$ is equal to the frequency of the first overtone of a closed pipe of length $l_c$. The value of $l_c$ in meters is:

The lengths of the two organ pipes open at both ends are $L$ and $(L+L_1)$. If they are sounded together,the beat frequency will be ($v=$ velocity of sound in air).

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

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $5 / x$. The value of $x$ is . . . . . . .

In a resonance tube,the first resonance is obtained when the level of water in the tube is at $16\,cm$ from the open end. Neglecting end correction,the next resonance will be obtained when the level of water from the open end is .... $cm$

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 ......... $cm$.