Question : An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of open pipe. The fundamental frequency of the open pipe is
a)200 Hz
b)300 Hz
c)240 Hz
d)480 Hz
Doubt by Sanya
Solution :
Let 𝜈 = frequency of open organ pipe
𝜈' = frequency of closed organ pipe
v = velocity of sound wave in air
L = Length of the organ pipe
n = mode of vibration
We know,
𝜈 = nv/2L
and
𝜈'=(2n-1)v/4L
Third Harmonic of Closed Organ Pipe occur at n=2 while for fundamental frequency of open organ pipe (n=1)
ATQ
𝜈2' = 100 + 𝜈1
[2(2)-1]v/4L=100+(1)v/2L
3v/4L=100+v/2L
3v/4L-v/2L=100
3v/4L-2v/4L=100
[Multiplying and dividing v/2L by 2]
v/4L=100
v/2L = 2×100
𝜈1 = 200 Hz
Hence, a)200 Hz, would be the correct option.