A closed pipe and an open pipe emit fundamental tones of the same frequency. Find out the ratio oftheirlengths.

A closed pipe and an open pipe emit fundamental tones of the same freq

1.	A closed pipe and an open pipe emit fundamental tones of the same frequency. Find out the ratio oftheirlengths.
Answer» Answer :Letthe LENGTH of the closed pipe and the open pipe be `l_(1) and l_(2)` , respectively . V is the velocity of sound in air. Forthe closed pipe, the fundamental frequency is ` n_(1) = (V)/(4l_(1))` ; for the open pipe, it is `n_(2) = (V)/(2l_(2))` Inthis problem, ` n_(1) = n_(2) `or,`(V)/(4l_(1)) = (V)/(2l_(2)) `or,`(l_(1))/(l_(2)) = (1)/(2)` Therefore, the ratio of their LENGTHS is 1 : 2 .