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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 n_{3} = n_{o}

where n_{3} = 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}=n_{3})

`thereforeL_o/L_3=1/8`

`therefore L_0:L_3=1:8`

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