In the fundamental mode,the time taken by the wave to reach the closed end of an air-filled pipe is $0.01 \ s$. The fundamental frequency is (in $Hz$)

$A$ pipe closed at one end has a length of $83 \ cm$. The number of possible natural oscillations of the air column whose frequencies lie below $1000 \ Hz$ are (velocity of sound in air $= 332 \ m/s$).

Give the equation for the normal modes of vibration for a closed pipe.

$A$ closed organ pipe $150 \ cm$ long gives $7$ beats per second with an open organ pipe of length $350 \ cm$,both vibrating in fundamental mode. The velocity of sound is . . . . . . $m/s$.

An organ pipe closed at one end has a fundamental frequency of $1500 \ Hz$. The maximum number of overtones generated by this pipe which a normal person can hear is ($A$ normal person can hear frequencies up to $19.5 \ kHz$,neglect end correction).

An air column is of length $17 \ cm$. The ratio of frequencies of the $5^{\text{th}}$ overtone for an air column closed at one end to that open at both ends is (velocity of sound in air $= 340 \ ms^{-1}$).