The human vocal tract is a pipe that extends about 17 cm from the lips to the vocal folds (also

1. First, we need to understand that the vocal tract is acting like a stopped pipe. In a stopped

The human vocal tract is a pipe that extends about 17 cm...

The human vocal tract is a pipe that extends about $17 \mathrm{~cm}$ from the lips to the vocal folds (also called "vocal cords") near the middle of your throat. The vocal folds behave rather like the reed of a clarinet, and the vocal tract acts like a stopped pipe. Estimate the first three standing-wave frequencies of the vocal tract. Use $v=344 \mathrm{~m} / \mathrm{s}$. (The answers are only an estimate, since the position of lips and tongue affects the motion of air in the vocal tract.)

Transcript

00:01 In this question, we are to model a vocal track using a pipe that is closed on one end and has a length of 0 .17 meters.

00:11 Well, for a pipe closed at one end, the closed end is not going to allow any motion, any lateral motion of the air molecules there.

00:20 So the air molecules are going to have a node there of motion.

00:24 However, on the other end, they're going to have the maximum amount of motion that they can have.

00:28 So we're going to go from a node to an antinode in our longest wavelength standing wave, which is one -fourth of the wavelength there.

00:40 If you go from node to an antinode.

00:42 So one -fourth of the wavelength is going to equal the length of the tube.

00:49 So therefore, the length of the wavelength is going to equal four times the length of the tube divided by one.

00:57 The next longest wave that you can have a standing wave in here is going to go from a node to an antinode back to a node and down to an antinode.

01:10 And that is going to be then three -fourths of a wave, basically.

01:13 That's what you've covered there so far.

01:16 So three -fourths of the wavelength is going to equal the length of the tube, which means that the wavelength of this one is going to equal four l.

01:28 Over 3.

01:29 Similarly here, we can go from a node to an antinode, down to a node to another anti -node, and up to a node, and to an antinode.

01:41 And that is basically, it is a five -fourths of a wave...

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