Many opera singers (and some pop singers) have a range of about 2 1 2 octaves or

Question

Many opera singers (and some pop singers) have a range of about

212 octaves or even greater. Suppose a soprano's range extends from A below middle C (frequency 220Hz ) up to Eb above high C (frequency 1244Hz ). Although the vocal tract is quite complicated, we can model it as a resonating air column, like an organ pipe, that is open at the top and closed at the bottom. The column extends from the mouth down to the diaphragm in the chest cavity, and we can also assume that the lowest note is the fundamental.

A) How long is this column of air if v= 354m/s?

L=?cm

B) does your result seem reasonable, on the basis of observations of your own body ?

Explanation / Answer

fundamental frequency =f1=V/(4*L)....

L=V/(2*f1)=354/(4*220)=0.402m=40.2 cm

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