contestada

An open organ pipe 30 cm long and a closed organ pipe 23 cm long, both of same diameter , are each sounding its first overtone , and these are in unison. What is the end correction of these pipes?

Respuesta :

First overtone of open organ pipe is given as

[tex]f_{1o} = \frac{v}{L_1 + 2e}[/tex]

first overtone of closed organ pipe is given as

[tex]f_{1c} = \frac{3v}{4(L_2 + e)}[/tex]

now they are in unison so we will have

[tex]\frac{v}{L_1 + 2e} = \frac{3v}{4(L_2 + e)}[/tex]

[tex]\frac{1}{30 + 2e} = \frac{3}{4(23 + e)}[/tex]

[tex]90 + 6e = 92 + 4e [/tex]

[tex]e = 1 cm[/tex]

so end correction of both pipes is e = 1 cm

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