If two successive resonant frequencies for an open ended organ pipe (open at both ends) are 387 Hz and 430 Hz, and the speed of sound in air is 343 m/s, determine the following.
(a) frequency of the fundamental
Hz
(b) length of the pipe
m
Steve4Physics
Favorite Answer
If the fundamental frequency is F, then the 2 harmonics are mF and nF where m and n are integers. They are successive, so n=m+1.
With a bit of factoring we get 387/430 = 9/10
m=9 and n=10.
The fundamental = 430/10 = 43Hz
(or use 387/9 = 43Hz)
Wavelength of fundamental λ = v/F = 343/43 = 7.98m
For both ends open,L = λ/2
L = 7.98/2 = 3.99m