Question : The third harmonic of a closed organ pipe is equal to the second overtone of an open organ pipe. If the length of the open organ pipe is 60 cm, then the length of closed organ pipe will be
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 = 60 cm
L' = Length of the closed organ pipe
n = mode of vibration
We know,
𝜈 = nv/2L
and
𝜈'=(2n-1)v/4L
Frequency of third harmonic (n=2) of a closed organ pipe = Frequency of second overtone (n=3) of an open organ pipe.
𝜈'2=𝜈3
{2(2)-1}v/4L'=3v/2L
3v/4L'=3v/2L
3/4L'=3/2L
1/2L'=1/L
L=2L'
L/2=L'
60/2=L'
L'=30 cm
Hence, (b) 30 cm, would be the correct option.
Similar Question :
The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L' metre long. The length of the open pipe will be
(a) L'/2
(b) 4L'
(c) L'
(d) 2L'