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
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Solution
Given that n3 = no
where n3 = frequency of the third overtone of the open pipe
no = 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)) `..........(∵ no=n3)
`thereforeL_o/L_3=1/8`
`therefore L_0:L_3=1:8`
Concept: Study of Vibrations of Air Columns
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