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 $... \ ms^{-1}$.

An open organ pipe is closed at one end such that the third overtone of the closed pipe is found to be higher in frequency by $200 \ Hz$ than the second overtone of the original open pipe. The fundamental frequency of the open pipe is (Neglect end correction). (in $Hz$)

In fundamental mode,the time required for the sound wave to reach up to the closed end of a pipe filled with air is $t$ seconds. The frequency of vibration of the air column is

In a pipe closed at one end, an air column is vibrating in the fourth overtone. If the vibrating air column has $x$ nodes and $y$ antinodes, then the values of $x$ and $y$ are respectively:

The pitch of an organ pipe is highest when the pipe is filled with

In the experiment for the determination of the speed of sound in air using the resonance column method,the length of the air column that resonates in the fundamental mode with a tuning fork is $0.1 \ m$. When this length is changed to $0.35 \ m$,the same tuning fork resonates with the first overtone. Calculate the end correction in $m$.