Question

The fundamental frequency of an air column in a pipe closed at one end is in unison with the third overtone of an open pipe. Calculate the ratio of lengths of their air columns

Answer 1

Given that n₃ = n_o
where n₃ = frequency of the third overtone of the open pipe
n_o = fundamental frequency of the closed pipe

Third overtone of open pipe is

`n_3=4(V/(2L_3))`

Fundamental frequency of closed pipe at one end is

`n_o=V/(4L_o)`

`V/(4L_o)=4(V/(2L_3)) `..........(∵ n_o=n₃)

`thereforeL_o/L_3=1/8`

`therefore L_0:L_3=1:8`