Two consecutive harmonics of an air column in a pipe closed at one end are of frequencies $150 \,Hz$ and $250 \,Hz$. The fundamental frequency of the air column is: (in $\,Hz$)

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 $Hz$)

$Assertion :$ The fundamental frequency of an open organ pipe increases as the temperature is increased.
$Reason :$ As the temperature increases,the velocity of sound increases more rapidly than the length of the pipe.

If we study the vibration of a pipe open at both ends,then the following statement is not true.

$A$ closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio:

$A$ string is stretched between fixed points separated by $75.0\, cm$. It is observed to have resonant frequencies of $420\, Hz$ and $315\, Hz$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is .... $Hz$.