When you speak, your vocal cords emit a range of frequencies as they vibrate. The sounds that are amplified are the natural resonances of your vocal tract. Although the vocal tract is quite complicated, we can model it as an open-closed tube starting at the opening of the mouth and ending on the diaphragm (the large muscle separating the abdomen and the chest cavity). a. What is the length of the vocal tract if its fundamental frequency is 250 Hz in air at 20 degrees Celsius? What is the wavelength of this fundamental frequency? b. Imagine now that you speak in the same way physically that you spoke in part a, but before speaking you breathe from a balloon filled with Helium, in which the speed of sound is roughly 1000 m/s. Now, what is the fundamental frequency of your vocal tract? What is the wavelength of this fundamental frequency?
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