27. || The vocal tract. Many opera singers (and some pop singers) have BIO a range of about 2 \frac{1}{2} octaves or even greater. Suppose a soprano's range extends from A below middle C (frequency 220 Hz) up to E-flat above high C (frequency 1244 Hz ). Although the vocal tract is quite complicated, we can model it as a resoNting 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. How long is this column of air if v=354 m/s ? Does your result seem reasoNble on the basis of observations of your own body?

Frequency refers to the number of waves that pass a fixed point in unit time. Frequency is denoted by the symbol f, and is measured in hertz (Hz).

Given,

f=220

velocity= 354 m/s

=> 220 = (nl)*(354)/(4*1)

=>1244 = (n2)*(354)/(4*1)

=> n2/n1= 5.65

=> n1=1, n2=6

=> = 40 cm (final answer).

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