An open pipe is suddenly closed at one end with the result that the frequency of the third harmonic of the closed pipe is found to be higher by $100 \ Hz$ than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is .... $Hz$.

If the seventh harmonic of a closed organ pipe is in unison with the fourth harmonic of an open organ pipe,then the ratio of the length of the closed pipe to that of the open pipe is:

$A$ student is performing the experiment of a resonance column. The diameter of the column tube is $6 \, cm$. The frequency of the tuning fork is $504 \, Hz$. The speed of sound at the given temperature is $336 \, m/s$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is..........$cm$.

$A$ flute,which we treat as a pipe open at both ends,is $34\, cm$ long. The fundamental frequency of the flute when all its holes are covered is .... $Hz$ [Take velocity of sound in air $= 340\, m/s$].

$A$ 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?

The frequency of the second overtone of an open pipe is equal to the frequency of the first overtone of a closed pipe. The ratio of the lengths of the open pipe to the closed pipe is