An organ pipe open at one end is vibrating in its first overtone and is in resonance with another pipe open at both ends vibrating in its third harmonic. The ratio of the length of the two pipes is:

An organ pipe has a fundamental frequency of $80 \ Hz$. If one end of the pipe is closed,what are the frequencies produced? (Neglect end correction)

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1:$ In the resonance tube experiment,if the tuning fork is replaced by another identical tuning fork but with its arms filed,the length of the air column should be increased to obtain resonance again.
Statement $2:$ On filing the arms,the frequency of a tuning fork increases.

In a resonance column lab experiment to measure the velocity of sound,the first resonance is obtained at a length $l_1$ and the second resonance at a length $l_2$. Then-

Two open organ pipes give $4$ beats/sec when sounded together in their fundamental modes. If the lengths of the pipes are $100 \ cm$ and $102.5 \ cm$ respectively,then the velocity of sound is ..... $m/s$.

While measuring the speed of sound by performing a resonance column experiment,a student gets the first resonance condition at a column length of $18 \ cm$ during winter. Repeating the same experiment during summer,she measures the column length to be $x \ cm$ for the second resonance. Then