Question : The second overtone of a pipe closed at one and has the same frequency as the third overtone of a pipe open at both ends. Compare the lengths of the pipes.
Let 𝜈 = frequency of open organ pipe
𝜈' = frequency of closed organ pipe
v = velocity of sound wave in air
L = Length of the open organ pipe
L' = Length of the closed organ pipe
n = mode of vibration
We know,
𝜈 = nv/2L
and
𝜈'=(2n-1)v/4L
Frequency of second overtone in Closed Organ Pipe = Frequency of third overtone in Open Organ Pipe
𝜈'3=𝜈4
[2(3)-1]v/4L' = 4v/2L
5v/4L' = 4v/2L
5/4L'=4/2L
5/2L'=4/L
L/L'=8/5
L'/L=5/8
L':L=5:8
Similar Question :
The second overtone of a closed organ pipe P1 and the third overtone of an open pipe P2 are in unison with a tuning fork. The ratio of the length of P1 and P2 will be
(a) 5:8
(b) 1:3
(c) 8:3
(d) 3:1