When you voice the vowel sound in "hat," you narrow the opening where your throat opens into the cavity of your mouth so that your vocal tract appears as two connected tubes. The first is in your throat, closed at the vocal cords and open at the back of the mouth. The second is the mouth itself, open at the lips and closed at the back of the mouth-a different condition than for the throat because of the relatively larger size of the cavity. The corresponding formant frequencies are \(800 \mathrm{~Hz}\) (for the throat) and \(1500 \mathrm{~Hz}\) (for the mouth). What are the lengths of these two cavities? Assume a sound speed of \(350 \mathrm{~m} / \mathrm{s}\)