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Chapter 2: Q27E (page 539)

BIO The Human Voice. The human vocal tract is a pipe that extends about 17 cm from the lips to the vocal folds (also called 鈥渧ocal cords鈥�) 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 m/s. (The answers are only an estimate, since the position of lips and tongue affects the motion of air in the vocal tract.)

Short Answer

Expert verified

The first three standing-wave frequencies of the vocal tract is 505.88鈥塇锄, 1517.65鈥塇锄 and 2529.41鈥塇锄.

Step by step solution

01

STEP-1: Given Data

Length of human vocal tract :L=17鈥塩尘=0.17鈥尘

Speed of sound in air: v=344鈥尘/s

02

STEP-2: Standing Waves

When two waves moving in the opposite direction and having the same amplitude and frequency, are superimposed on each other, the resultant wave is known as a standing wave.

03

STEP-3: Calculating the first three frequencies of the vocal tract.

The first three standing waves in a stopped pipe are n=1,鈥�n=3鈥嬧赌塧苍诲鈥�n=5. Here n is the number of harmonics. The frequency of the nth harmonic is given as-

f=v位=nv4L

f1=nv4L=1脳344鈥尘/s4脳(17脳10鈭�2鈥尘)=505.88鈥塇锄f3=nv4L=3脳344鈥尘/s4脳(17脳10鈭�2鈥尘)=1517.65鈥塇锄f5=nv4L=5脳344鈥尘/s4脳(17脳10鈭�2鈥尘)=2529.41鈥塇锄

Therefore. the first three standing-wave frequencies of the vocal tract is 505.88鈥塇锄, 1517.65鈥塇锄 and 2529.41鈥塇锄.

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Most popular questions from this chapter

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