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 experiment,two consecutive resonances are observed when the lengths of the air columns are $16 \ cm$ and $49 \ cm$. If the frequency of the tuning fork used is $500 \ Hz$,the velocity of sound in air is $... \ ms^{-1}$.

$A$ tuning fork vibrating with a frequency of $512$ $Hz$ is kept close to the open end of a tube filled with water. The water level in the tube is gradually lowered. When the water level is $17$ $cm$ below the open end,maximum intensity of sound is heard. If the room temperature is $20^{\circ} C$,calculate:
$(a)$ Speed of sound in air at room temperature.
$(b)$ Speed of sound in air at $0^{\circ} C$.
$(c)$ If the water in the tube is replaced with mercury,will there be any difference in your observations?

$A$ pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to

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:

$A$ pipe $P_{C}$ closed at one end and a pipe $P_{O}$ open at both ends are vibrating in their second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe $P_{C}$ to $P_{O}$ is (Neglect end correction):