The `p^(th)` overtone of an organ pipe open at both ends has a frequency `n_(1)` . What one end of the pipe is closed , its `q^(th)` overtone has a fr

Question

The `p^(th)` overtone of an organ pipe open at both ends has a frequency `n_(1)` . What one end of the pipe is closed , its `q^(th)` overtone has a fr

The `p^(th)` overtone of an organ pipe open at both ends has a frequency `n_(1)` . What one end of the pipe is closed , its `q^(th)` overtone has a frequency `n_(2)`. What is the value of `n_(1)/n_(2)` ?

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Let L be the length of an orgin pipe and v the speed of sound in air.
When the pipe has both its ends open, the frequency of the pth overtone, ignoring the end correction, is
`n=(+1)(v)/(2L)" or "(v)/(2L)=(n)/(p+1)" "`…..(1)
When one end of the pipe is closed, ignoriung the end correction, the frequency of the qth overtone of a pipe of length L and closed at one end is
`N=(2q+1)(v)/(4L)=(2q+1)/(2).(v)/(2L)`
`:. N=((2q+1)n)/(2(p+1))" "`....[from Eq.(1)]
which is the required expression.