1604 Standing Sound Waves and Normal Modes

Exercises

25, 27, 29
16.25 Standing sound waves are produced in a pipe that is $1.20 m$ long. For the fundamental and first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes and the pressure nodes if (a) the pipe is open at both ends and (b) the pipe is closed at the left end and open at the right end.

16.27 .The Human Voice. The human vocal tract is a pipe that extends about $17 \text{ cm}$ 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 $v = 344 \text{ m/s}$. (The answers are only an estimate, since the position of lips and tongue affects the motion of air in the vocal tract.)

16.29 The longest pipe found in most medium-size pipe organs is $4.88 m$ (16 ft) long. What is the frequency of the note corresponding to the fundamental mode if the pipe is (a) open at both ends, (b) open at one end and closed at the other?