Answer:
f = 409 Hz
Explanation:
We have,
Length of the open organ pipe, l = 0.29 m
Frequency of vibration of second overtone, [tex]f_2 = 1227 Hz[/tex]
It is required to find the fundamental frequency of the pipe. For the open organ pipe, the frequency of second overtone is given by :
[tex]f_2=\dfrac{3v}{2l}[/tex]
v is speed of sound
Let f is the fundamental frequency. It is given by :
[tex]f=\dfrac{v}{2l}[/tex]
The relation between f and f₂ can be written as :
[tex]f_2=3f\\\\f=\dfrac{f_2}{3}\\\\f=\dfrac{1227}{3}\\\\f=409\ Hz[/tex]
So, the fundamental frequency of the pipe is 409 Hz.
