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

Answer

Let the length of the closed pipe and the open pipe be `l_(1) and l_(2)` , respectively . V is the velocity of sound in air.
For the closed pipe, the fundamental frequency is ` n_(1) = (V)/(4l_(1))` ;
for the open pipe, it is `n_(2) = (V)/(2l_(2))`
In this 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 .