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 220 Hz ) up to Eb above high C (frequency 1244 Hz ). 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.   

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

Does your result seem reasonable, on the basis of observations of your own body ?

Answer 1

Part a Resonance frequency of the closed organ pipe is defined as, f. 42 Here n= 1,3,5,..... etc. v = speed of sound = 354 m/s L = length of the pipe for fundamental frequency, n = 1 Fundamental frequency of the pipe is could be written as T=AL

L=V According to the question, lowest frequency is the fundamental frequency, so, fundamental frequency = f = 220 Hz now, lets plug this value in the above equation, L= 354 m/s 4 (220 Hz) L=0.40 m Ans. So, column of the air = 0.40 m Part b

Normal height of the person is around 1.50 m. we have found the average length of the pipe as 0.40 m which is small to the height of the person. So, yes, it is reasonable height in comparison to the height of the person.