Question

Estimate the first three standing-wave frequencies of the vocal tract. use v=344m/s. (the answers are only an estimate, since the position of lips and tongue affects the motion of air in the vocal tract.)

Answer 1

Vocal tract behaves like a stopped pipe.
The fundamental frequency for a stopped pipe is given with the following formula:

`f_0=(v)/(4L)`
Higher harmonics are simply:

`f=nf_0; n=1,3,5,7,9...`
Keep in mind that the stopped pipe produces only odd harmonics.
Lenght of a human vocal tract is 17cm(for males, females have slightly shorter vocal tract). We can now calculate the answers.

`f_0=(344)/(4\cdot 0.17)=505.88$Hz`
Now we can calculate higher harmonics:

`f_3=3f_0=1517.64$Hz`

`f_5=5f_0=2529.4$Hz`