Compare the fundamental frequencies of the tones emitted by two pipes of equual length, one open at both ends and the other closed at one end.

Answer

Let V be the velocity of sound in air and l, the length of each of the pipes,
`:.` The frequency of the fundamental tone emitted by the pipe open at both ends, ` n_(1) = (V)/(2l)` ;
and the frequency of the fundamental tone emitted by the pipe closed at one end , `n_(2) = (V)/(4l)*`
`:. (n_(1))/(n_(2)) = (V/(2l))/(V/(4l)) = 2 or , n_(1) = 2n_(2)`
So, the fundamental frequency for a pipe open at both ends is twice of a pipe of the same length, but closed at one end .